Active inductors and their application circuits

Abstract

This product provides an active inductor that can achieve the functionality of a high-inductance signal inductor, which is difficult to obtain and expensive, using a simple circuit. [Solution] The configuration involves connecting a first feedback resistor (Rf) between the output of the main amplifier and the inverting input, and using the inverting input of the main amplifier as the input and the output of the main amplifier as the output, as an active inductor with voltage input and voltage output.

Description

[Technical Field]

[0001] The present invention relates to an active inductor using an amplifier, and to a filter and composite amplifier using the same. [Background technology]

[0002] Figure 1 of Patent Document 1 shows an example of a composite amplifier circuit (composite amplifier) ​​that uses amplifier 1, which is an AC amplifier that handles the high frequency range, and amplifier 2, which is a DC amplifier that handles the low frequency range including DC, and has an output that combines the characteristics of amplifier 1 and amplifier 2.

[0003] Furthermore, Figure 1 of Patent Document 2 shows an example of a broadband measurement amplifier (composite amplifier) ​​in which an input signal from input terminal IN is commonly supplied to the inputs of a DC amplifier 21 and an AC amplifier 22, a low-pass filter 23 is connected to the output of the DC amplifier 21, a high-pass filter 24 is connected to the output of the AC amplifier 22, and the output signals of the low-pass filter 23 and the high-pass filter 24 are combined by connecting them to the input of an adder 25, and the output of the adder 25 is output from the output terminal OUT.

[0004] While composite amplifiers are one application of the active inductor of the present invention, all of these patent documents use demultiplexers with passive elements, and no active inductor like the one of the present invention was used.

[0005] Patent Document 3 describes an amplifier circuit in which the DC open-loop gain is enhanced by stacking the output of a band-limiting amplifier circuit with the output of a main amplifier circuit. This circuit is suitably applicable when a large DC open-loop gain is required for use in the active inductor of the present invention.

[0006] Non-patent document 1 is an example of a real-world inductor. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Application Publication No. 57-211812 [Patent Document 2] Japanese Patent Application Publication No. 01-086035 [Patent Document 3] Japanese Patent Publication No. 2024-065053 [Non-patent literature]

[0008] [Non-Patent Document 1] Specification sheet for Taiyo Yuden Co., Ltd.'s "LSRNJ10145GL152MNY" https: / / ds.yuden.co.jp / TYCOMPAS / jp / detail?pn=LSRNJ10145GL152MNY&u=M [Overview of the project] [Problems that the invention aims to solve]

[0009] Figure 1 and its description in Patent Document 1 use a passive inductor. Patent Document 2 also exemplifies the use of a first-order filter as a low-pass filter 23, suggesting the use of a passive inductor in a similar manner. However, neither example specifies the inductance, nor does it indicate that the inductance is variable. Furthermore, neither example mentions any consideration of impedance matching for the composite amplifier.

[0010] In particular, commercially available signal inductors have few inductances of several hundred μH or more, and their shape is large, resulting in high costs and low self-resonant frequencies. Furthermore, commercially available signal inductors have a large tolerance of ±10% in some cases, yet the inductance is a fixed value, and it is not possible to adjust the inductance to achieve the desired characteristics. [Means for solving the problem]

[0011] To solve the above problems, the present invention provides an active inductor with voltage input and voltage output, in which a first feedback resistor (Rf) is connected between the output and inverting input of the main amplifier, and the inverting input of the main amplifier is used as the input and the output of the main amplifier is used as the output.

[0012] In the active inductor according to the present invention, the main amplifier can be an inverting amplifier circuit that limits the gain by providing a gain resistor (Rg') and a second feedback resistor (Rf').

[0013] In the active inductor according to the present invention, the main amplifier can be an inverting integrating circuit with a gain resistor (Rg') and a feedback capacitance (Cf') to limit the bandwidth.

[0014] In the active inductor according to the present invention, the main amplifier can be an inverting imperfect integrator circuit that limits the gain and bandwidth by comprising a gain resistor (Rg'), a second feedback resistor (Rf'), and a feedback capacitance (Cf').

[0015] In the active inductor according to the present invention, an RC low-pass filter (R) is placed between the output of the main amplifier and the output of the active inductor. LPF , C LPF ) is provided to limit the bandwidth, and the single gain frequency (f) of the active inductor is limited. T ) can be set to be lower than the cutoff frequency (fc) of the main amplifier.

[0016] In the active inductor according to the present invention, an amplification element can be added between the input of the active inductor and the input of the main amplifier.

[0017] In the active inductor according to the present invention, an amplification element can be added between the output of the main amplifier and the output of the active inductor.

[0018] The present invention also provides a low-pass filter using the active inductor.

[0019] The present invention also provides a bandpass filter using the active inductor, further comprising a capacitive element on the input side.

[0020] The present invention also provides a composite amplifier comprising a low-pass filter using an active inductor, a CR high-pass filter, and a high-pass filter using a second main amplifier.

[0021] The present invention also provides a composite amplifier comprising a low-pass filter using the active inductor, a band-pass filter using the active inductor further equipped with a capacitive element on the input side, and a high-pass filter using a CR high-pass filter and a second main amplifier. [Effects of the Invention]

[0022] The active inductor of the present invention has the effect of realizing the functionality equivalent to that of a large-inductance signal inductor, which is difficult to obtain and expensive, with a simple circuit.

[0023] Furthermore, the active inductor of the present invention has the effect of realizing a function equivalent to that of a variable inductor, which is hardly commercially available, with a simple circuit without generating a self-resonant frequency.

[0024] Furthermore, the active inductor of the present invention has the effect of enabling the implementation of low-pass filters and band-pass filters with simple circuits. Moreover, by using it in combination with a high-pass filter, it has the effect of enabling the implementation of composite amplifiers matched to 50Ω, such as composite amplifiers for audio applications. [Brief explanation of the drawing]

[0025] [Figure 1] (A) A basic circuit of the active inductor of the present invention, (B) an equivalent circuit of the active inductor, and (C) an equivalent circuit using a real inductor. [Figure 2] (A) Examples of frequency characteristics of gain for a basic active inductor circuit, an equivalent circuit using an ideal inductor, and an equivalent circuit using a real inductor; (B) Examples of frequency characteristics of input impedance for a basic active inductor circuit, an equivalent circuit using an ideal inductor, and an equivalent circuit using a real inductor. [Figure 3] (A) An example of a circuit in which gain limiting is performed on an active inductor, and (B) An example of a circuit in which an amplification element is added to the gain limiting on an active inductor. [Figure 4] (A) An example of the frequency characteristics of the gain of a circuit with gain limiting using an active inductor, and (B) An example of the frequency characteristics of the input impedance of a circuit with gain limiting using an active inductor. [Figure 5] This figure shows an example of a circuit with bandwidth limiting applied to an active inductor. [Figure 6] (A) An example of the frequency characteristics of the gain of a circuit with band-limiting applied to an active inductor, and (B) An example of the frequency characteristics of the input impedance of a circuit with band-limiting applied to an active inductor. [Figure 7] This figure shows an example of a circuit in which gain limiting and bandwidth limiting are performed on an active inductor. [Figure 8] (A) An example of the frequency characteristics of the gain of a circuit in which gain limiting and bandwidth limiting are performed using an active inductor, and (B) An example of the frequency characteristics of the input impedance of a circuit in which gain limiting and bandwidth limiting are performed using an active inductor. [Figure 9] This figure shows an example of a circuit with a different bandwidth limiting applied to an active inductor. [Figure 10] (A) An example of the frequency characteristics of the gain of a circuit with an active inductor that has been subjected to another band limiting method, and (B) An example of the frequency characteristics of the input impedance of a circuit with an active inductor that has been subjected to another band limiting method. [Figure 11]This figure shows the equivalent circuits of (A) an LR low-pass filter circuit, (B) a CLR band-pass filter circuit, and (C) a CR high-pass filter circuit. [Figure 12] (A) An example of a low-pass filter circuit using an active inductor, (B) An example of a band-pass filter circuit using an active inductor, and (C) An example of a high-pass filter circuit using a CR high-pass filter and a second main amplifier. [Figure 13] (A) An example of the frequency characteristics of the gain of the equivalent circuit of a CLR bandpass filter, and (B) An example of the frequency characteristics of the input impedance of the equivalent circuit of a CLR bandpass filter. [Figure 14] (A) An example of the frequency characteristics of the gain of a bandpass filter circuit using an active inductor, and (B) An example of the frequency characteristics of the input impedance of a bandpass filter circuit using an active inductor. [Figure 15] This figure shows an example of a composite amplifier with impedance matching. [Figure 16] (A) An example of the frequency characteristics of the gain of a composite amplifier with impedance matching, and (B) An example of the frequency characteristics of the input impedance of a composite amplifier with impedance matching. [Figure 17] This figure shows an example of a composite amplifier with impedance matching using the active inductor of the present invention. [Figure 18] (A) An example of the frequency characteristics of the gain of a composite amplifier with impedance matching using the active inductor of the present invention, and (B) An example of the frequency characteristics of the input impedance of a composite amplifier with impedance matching using the active inductor of the present invention. [Figure 19] This figure shows an example of a 3-way multi-amplifier circuit for audio use, employing an LR low-pass filter circuit, a CLR band-pass filter circuit, and a CR high-pass filter circuit. [Figure 20](A) An example of the frequency characteristics of the gain of a 3-way multi-amplifier circuit for audio, and (B) An example of the frequency characteristics of the input impedance of a 3-way multi-amplifier circuit for audio. [Figure 21] This figure shows an example of a 3-way multi-amplifier circuit for audio applications, in which the active inductor of the present invention is used in the LR low-pass filter circuit and the CLR band-pass filter circuit. [Figure 22] (A) An example of the frequency characteristics of the gain of a 3-way multi-amplifier circuit for audio using the active inductor of the present invention, and (B) An example of the frequency characteristics of the input impedance of a 3-way multi-amplifier circuit for audio using the active inductor of the present invention. [Modes for carrying out the invention]

[0026] Preferred embodiments of the present invention will be described below with reference to the drawings. However, the present invention is not limited to the following description, and various modifications and changes are possible for those skilled in the art based on the gist of the invention as described in the claims or disclosed in the embodiments for carrying out the invention. Such modifications and changes are also within the scope of the present invention. Furthermore, all documents referenced herein are incorporated herein by reference in their entirety.

[0027] <Common matters> The active inductor of the present invention may sometimes be simply referred to as an active inductor.

[0028] Furthermore, in the following explanations, the type of frequency and signal name may be omitted, and only the symbol may be indicated. For example, the cutoff frequency fc may be simply written as fc, and the feedback resistor Rf may be simply written as Rf. Also, a single notation may indicate either the signal name or its value. For example, the output signal Vout may be used as the signal name, or its voltage may be written as Vout.

[0029] In this invention, as a general rule, "amplifier" refers to a single functional block having an amplification function, and "amplification circuit" refers to a functional block that has an amplification function as a whole through a combination of amplifiers, passive elements, etc.

[0030] The "amplifiers" illustrated in the explanations and diagrams are, in principle, voltage-feedback operational amplifiers with finite open-loop gain and finite single-gain frequency, and all other performance characteristics, unless otherwise specified, are, in principle, those of an "ideal operational amplifier." However, the voltage-feedback operational amplifier is just one example, and other types of amplifiers can be used in this invention if they meet the requirements. (As a specific example, a current-feedback operational amplifier can be used as the amplifier for the active inductor in this invention if the frequency characteristics of the gain decrease at a rate of 20 dB / decade above the cutoff frequency fc.) The amplifier is not limited to operational amplifier ICs; amplifiers composed of discrete components can also be used. Furthermore, a single amplification circuit or a combination of multiple amplification circuits can be used in place of an amplifier.

[0031] In amplifiers U, amplifier U', etc., unless otherwise specified, the DC gain G DC The gain is 60dB, the cutoff frequency fc is 10kHz, and the single gain frequency f T 10MHz is used as an example.

[0032] The "amplifying elements" (represented by a right-pointing triangle symbol with 1 input and 1 output, and the amplification factor displayed inside the triangle symbol), mainly illustrated in equivalent circuits, are, in principle, ideal amplifiers with infinite input impedance, 0Ω output impedance, and infinite bandwidth.

[0033] In the circuit diagram, the reference potential (downward triangle symbol) is assumed to be 0V, but it does not necessarily have to be 0V, and it may also be connected to the reference potential in an AC manner.

[0034] An "RC low-pass filter" refers to a low-pass filter using a resistor R and a capacitance C; an "LR low-pass filter" refers to a low-pass filter using an inductor L and a resistor R; a "CLR band-pass filter" refers to a band-pass filter using a capacitance C, an inductor L, and a resistor R; and a "CR high-pass filter" refers to a high-pass filter using a capacitance C and a resistor R. Each of these may also include an amplifier or amplification element.

[0035] Furthermore, when the active inductor of the present invention is used as an LR low-pass filter as is, it should generally be described as "a low-pass filter using an active inductor." When the active inductor of the present invention is used as a CLR band-pass filter by adding a capacitance C to the input, it should generally be described as "a band-pass filter using an active inductor."

[0036] The formulas presented are "theoretical formulas" or "approximation formulas," and actual characteristics may not be exactly as shown in the formulas.

[0037] The frequency response graphs are the results of simulations performed using Analog Devices' "LTSpice". In the gain frequency response graph, the horizontal axis is frequency displayed logarithmically, and the vertical axis is gain. When the input and output polarities are reversed, the gain will be a negative value, but in the gain frequency response graph, following convention, the sign is not considered, and the absolute value of the amplification factor is used. In the input impedance frequency response graph, the horizontal axis is frequency displayed logarithmically, and the vertical axis is the input impedance Zin as seen from the input -Vin.

[0038] <Invention details> The details of the present invention are described below.

[0039] (First Embodiment) <1. Basic Circuit for Active Inductor> <1.1 Basic Configuration of an Active Inductor> First, the basic configuration and function of the active inductor of the present invention will be described.

[0040] Figure 1(A) shows the basic circuit of the active inductor of the present invention, which consists of an amplifier U and a feedback resistor Rf. Figure 1(B) shows the equivalent circuit of the basic circuit configuration of the active inductor of the present invention. Figure 1(C) shows the equivalent circuit when using a real inductor.

[0041] Figure 2(A) shows examples of the frequency characteristics of the gain of the basic circuit of the active inductor of the present invention, the equivalent circuit using an ideal inductor, and the equivalent circuit using a real inductor, while Figure 2(B) shows examples of the frequency characteristics of each input impedance.

[0042] The basic circuit configuration of the active inductor of the present invention shown in Figure 1(A) is commonly known as the basic circuit configuration of a current amplifier circuit. However, in the present invention, this circuit configuration is used not as a current amplifier circuit, but to realize a function equivalent to an LR low-pass filter circuit, representing a different technical concept from that of a current amplifier circuit.

[0043] The current amplifier circuit's input is a current signal, while the active inductor of this invention's input is a voltage signal, which is another fundamental difference. In other words, although the circuit diagram may look the same as that of a current amplifier circuit, the intended function and operation are fundamentally different, and it is not simply a matter of choosing the right application.

[0044] Furthermore, in a current amplification circuit, the closer the amplifier U is to a so-called "ideal amplifier" (gain = ∞, input impedance = ∞, output impedance = 0Ω, bandwidth = ∞), the closer it approaches an ideal current amplification circuit. In contrast, the active inductor of the present invention assumes that both the gain and single-gain frequency in DC are "finite," and utilizes this property to realize the active inductor function. In this respect as well, it represents a different technical concept from a current amplification circuit.

[0045] <1.2 Examples of Characteristics of Basic Circuits, etc., of Active Inductors> In the graphs in Figures 2(A) and 2(B), the basic circuit characteristics of the active inductor of the present invention, the characteristics of the equivalent circuit using an ideal inductor, and an example of the characteristics of the equivalent circuit using a real inductor are superimposed.

[0046] Figures 2(A) and 2(B) show the circuit constants, etc., that form the basis of the characteristics illustrated in the graphs, as shown in Figures 1(A), 1(B), and 1(C).

[0047] In Figure 1(A), the amplifier U, as described in the "Common Specifications" section above, is used in an open-loop state as the amplification circuit. The feedback resistor Rf is set to 100.1 kΩ as an example.

[0048] In Figure 1(B), which uses an ideal inductor, the inductance of inductor L is assumed to be approximately 1592 μH, and the resistance R is assumed to be 100 Ω. These constants are the same as the equivalent constants of L and R obtained by converting from the constants in Figure 1(A) using the formula described later.

[0049] In Figure 1(C), which uses a real inductor, the inductor L is the equivalent circuit inductor shown within the dashed-dotted line in Figure 1(C). The characteristics of this real inductor were selected to be close to the ideal inductor of approximately 1592 μH in Figure 1(B), and the characteristics of Taiyo Yuden Co., Ltd.'s "LSRNJ10145GL152MNY" were used as an example. The inductor Ls was set to 1500 μH, the resistance Rs to 3.7 Ω, and the capacitance Cp calculated from the self-resonant frequency of 1.5 MHz to 7.5 pF. The resistance R was set to 96.3 Ω, which is 100 Ω minus the resistance Rs of 3.7 Ω.

[0050] The graph in Figure 2(A) shows an example of the frequency characteristics of the gain.

[0051] In the graph of Fig. 2(A), the solid line plot that decreases at 20 dB / decade (≈6 dB / octave) above the cut-off frequency fc (10 kHz) represents the characteristics of the basic circuit of the active inductor of the present invention in Fig. 1(A). In the basic circuit of the active inductor of the present invention in Fig. 1(A), an amplifier in an open-loop state is exemplified as the amplifier U. At frequencies sufficiently lower than the cut-off frequency fc, the open-loop gain exhibits a substantially constant gain of the DC gain G DC . (In an operational amplifier using an integrated circuit, G DC is generally on the order of several tens of dB to one hundred and several tens of dB). At frequencies sufficiently higher than the cut-off frequency fc, the gain is inversely proportional to the frequency and decreases at 20 dB / decade as shown in the figure as the frequency increases. The frequency at which the gain becomes 0 dB is the single gain frequency f T (10 MHz). (f T is also referred to as the transition frequency.)

[0052] In the graph of Fig. 2(A), the dashed line plot that decreases at 20 dB / decade above the cut-off frequency fc represents the characteristics of the equivalent circuit in Fig. 1(B) when an ideal inductor is used. However, since it overlaps with the solid line plot, it is almost indistinguishable. That is, the characteristics of the active inductor of the present invention shown in Fig. 1(A) are consistent with the equivalent circuit in Fig. 1(B) with L and R converted by the formula described later, which verifies the appropriateness of the formula described later.

[0053] In the graph of Fig. 2(A), the dash-dotted line plot having a dip at 1.5 MHz is an example of the characteristics of the equivalent circuit using the actual inductor shown in Fig. 1(C). For the equivalent inductance of approximately 1592 μH in Fig. 1(A), the actual inductor is 1500 μH. Due to this difference in inductance, the cut-off frequency fc has increased from 10 kHz to approximately 10.61 kHz. The 1.5 MHz of the dip is the self-resonance frequency of the actual inductor.

[0054] The graph in Figure 2(B) shows an example of the frequency characteristics of the input impedance. At frequencies well below the cutoff frequency fc, the input impedance Zin shows a constant value, exhibiting a frequency characteristic similar to that of a 100Ω resistor R in this example.

[0055] In the graph of Figure 2(B), of the two plots where the input impedance Zin increases by 20 dB / decade above the cutoff frequency fc (10 kHz), the solid line plot represents the characteristics of the basic circuit of the active inductor of the present invention shown in Figure 1(A), and the dashed line plot represents the characteristics of the equivalent circuit shown in Figure 1(B) when an ideal inductor is used.

[0056] In the equivalent circuit shown in Figure 1(B) when an ideal inductor is used, the single gain frequency f T Even at frequencies higher than this, the input impedance Zin continues to rise at a rate of 20 dB / decade. In contrast, in the basic circuit of the active inductor of the present invention, a single gain frequency f T At frequencies higher than this, the input impedance Zin asymptotically approaches the value of the feedback resistance Rf in Figure 1(A) (100.1kΩ in this example). This is the only difference between the active inductor of the present invention and the equivalent circuit using an ideal inductor. Hereafter, in the active inductor of the present invention, the asymptotic approach of the input impedance Zin to a constant resistance value at high frequencies may be referred to as "Zin plateauing."

[0057] -It is also possible to add a resistor (not shown in the diagram) immediately after Vin to bear a portion of the input impedance Zin. However, this is often undesirable because it changes the resistance value that Zin asymptotically approaches, so the explanation of this resistor will be omitted in the following examples.

[0058] In the graph in Figure 2(B), the dashed-dotted line plot with a peak at approximately 1.5 MHz represents an example of the characteristics of an equivalent circuit using a real inductor shown in Figure 1(C). At the self-resonant frequency of 1.5 MHz of the real inductor L exemplified, the impedance peak is shown due to the parallel resonance of Ls and Cp as shown in Figure 1(C). At frequencies sufficiently higher than the self-resonant frequency, the impedance drops by 20 dB / decade, meaning it functions as a capacitance C.

[0059] In the circuit shown in Figure 1(A), the single gain frequency f T It functions similarly to an ideal inductor up to nearly 10 MHz. In contrast, in the example of the characteristics of an equivalent circuit using a real inductor shown in Figure 1(C), it ceases to function as an inductor L at frequencies above approximately 1 MHz, which is lower than the self-resonant frequency of 1.5 MHz, and the circuit in Figure 1(A) shows higher performance. In other words, the active inductor of the present invention has the excellent effect of performing better than a real LR low-pass filter, especially when the inductance of the inductor L is large.

[0060] <1.3 Details of Active Inductors> Next, the details of the active inductor of the present invention will be described.

[0061] In the circuit shown in Figure 1(A), if the feedback resistance is Rf and G is the absolute value of the amplifier gain at that frequency, the input impedance Zin can be expressed as shown in equation (1).

[0062]

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[0063] In the basic circuit characteristics of the active inductor of the present invention shown in Figure 2(B), the single gain frequency f T At frequencies higher than f, the input impedance Zin asymptotically approached the value of the feedback resistor Rf in Figure 1(A) (100.1kΩ in this example). This is because f TAt frequencies higher than this, G becomes less than 1 (0 dB), and as a result the denominator of equation (1) approaches 1, Zin asymptotically approaches Rf.

[0064] At frequencies well below the cutoff frequency fc, the input impedance Zin becomes a resistance R (unit: Ω), and the feedback resistance Rf and DC gain G DC It can be expressed as shown in equation (2).

[0065]

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[0066] At frequencies exceeding the cutoff frequency fc, the input impedance Zin is proportional to the frequency and increases by 20 dB / decade as the frequency increases, as shown in Figure 2(B). This frequency-proportional impedance is the impedance characteristic of the inductor L itself. (The unit of the inductor L is H (Henry).) If we consider the inductor L and resistor R (see Figure 1(B)) as an LR low-pass filter, its cutoff frequency fc can be expressed as shown in equation (3).

[0067]

number

[0068] On the other hand, DC gain G DC and single gain frequency f T Therefore, the cutoff frequency fc can be expressed as shown in equation (4).

[0069]

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[0070] From equations (3) and (4), the inductor L can be expressed as shown in equation (5).

[0071]

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[0072] Furthermore, by applying equation (2), the inductor L can also be expressed as shown in equation (6).

[0073]

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[0074] DC gain G DC When is sufficiently greater than 1, the DC gain G DC / (1+DC gain G DC Since the value of the term ) approaches 1, the inductor L is L ≈ Rf / 2πf T This can be expressed as follows. For this reason, an even larger DC gain G DC When necessary, the circuit scheme described in Patent Document 3 can also be applied.

[0075] The feedback resistor Rf has the advantage of allowing the input impedance Zin to be easily changed, either partially or entirely, as shown in equations (1) and (2). It also has the advantage of allowing the equivalent inductance to be easily changed, as shown in equation (6).

[0076] The circuit in Figure 1(A) can be represented by an equivalent circuit as shown in Figure 1(B).

[0077] However, in the equivalent circuit of Figure 1(B) when L is an ideal inductor, Zin will continue to rise at a rate of 20 dB / decade as the frequency increases. In contrast, in the circuit of Figure 1(A), as shown in Figure 2(B), the single gain frequency f T At frequencies sufficiently higher than f, the input impedance Zin asymptotically approaches a constant value (the resistance of the feedback resistor Rf). This is because at a single gain frequency f T At frequencies higher than this, the gain of amplifier U becomes less than 1, and therefore it does not have an amplifying function, thus approaching the state where the input and output are connected by a feedback resistor Rf.

[0078] In the circuit shown in Figure 1(A), where the solid lines in Figures 2(A) and 2(B) represent the characteristics, Rf = 100.1kΩ and from equation (2), R = 100Ω. Also, the DC gain G DC =60dB (1000 times), single gain frequency f T From equation (5) and =10MHz, we get L ≈ 1592μH.

[0079] As described in detail above, the active inductor of this embodiment has a configuration in which a first feedback resistor (Rf) is connected between the output and the inverting input of the main amplifier, and is an active inductor with voltage input and voltage output, taking the inverting input of the main amplifier as the input and the output of the main amplifier as the output.

[0080] (Second Embodiment) <2. Amplifier Gain Limitation> <2.1 Overview of Amplifier Gain Limitation> As mentioned above, in the circuit of Figure 1(A), the amplifier U was used in an open-loop state. However, in a commonly used amplifier U, the DC gain G DC In some cases, the open-loop DC gain G of amplifier U is too large. DC It is set to 60dB (1000 times), and as a typical operational amplifier, G DC The difference was small. However, even in such examples, a small input offset voltage of 1mV resulted in a large output offset voltage of 1V, making it practically unusable. Also, the DC gain G DC In general, there were problems such as large variations between devices and susceptibility to temperature changes. Furthermore, for example, in order to make the input impedance Zin 10kΩ, the feedback resistor Rf had to be 1001 times 10kΩ, or 10.01MΩ (see equations (1) and (2)), and the resistance value Rf tended to be too high for a feedback resistor Rf used in a typical operational amplifier.

[0081] To solve these problems, an inverting amplifier circuit with a DC gain smaller than that of the open-loop configuration can be used as amplifier U in Figure 1(A) by using a gain resistor Rg', a feedback resistor Rf', and an amplifier U'. In this invention, this method will be referred to as "gain limiting".

[0082] Figure 3(A) shows an example of a circuit with gain limiting performed by an inverting amplifier. The input impedance of the inverting amplifier is equal to or slightly larger than the gain resistance Rg', which in turn lowers the input impedance Zin of the active inductor.

[0083] In the inverting amplifier circuit shown in Figure 3(A), if we set β' = Rg' / (Rg'+Rf') and G' is the absolute value of the gain of amplifier U' at that frequency, then the gain G of the amplifier U due to the inverting amplifier circuit at that frequency is given by equation (7). Also, the input impedance Zin' of the inverting amplifier circuit at that frequency is given by equation (8).

[0084]

number

[0085]

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[0086] When G' is sufficiently greater than 1 (especially when β' is large), G ≈ -(Rf' / Rg') and Zin' ≈ Rg'. A larger β' results in a wider bandwidth for the inverting amplifier circuit and also makes it less susceptible to variations and changes in G'.

[0087] Then, the input impedance Zin of the active inductor in Figure 3(A) is the parallel impedance of the right-hand side of equation (1) and Zin' in equation (8).

[0088] When it is necessary to eliminate the influence of the input impedance Zin' of the inverting amplifier circuit and bring the input impedance Zin of the active inductor close enough to equation (1), an amplification element (non-inverting) can be added as shown in the parentheses on the left side of Figure 3(B). Furthermore, when reducing the gain of the inverting amplifier circuit to achieve a wide bandwidth results in insufficient gain, or when the load-driving capability of U' is insufficient, an amplification element (non-inverting) can also be added as shown in the parentheses on the right side of Figure 3(B). (When adding amplification elements in both parentheses on the left and right sides of Figure 3(B), it is possible to make both inverting types if necessary.)

[0089] Such an amplification element needs to have a sufficiently wider bandwidth than the inverting amplifier circuit using U', and the absolute value of the amplification factor can be 1x or something other than 1x. As an example of such an amplification element, a non-inverting amplifier circuit using the operational amplifier U'', which has a wider bandwidth than U', can be used. (A voltage follower circuit with a gain of slightly less than 1x is an example of a non-inverting amplifier circuit.)

[0090] The addition of such amplification elements is applicable to all examples of active inductors described later, but explanations regarding the addition of amplification elements in subsequent examples will be omitted in principle.

[0091] In a commonly used non-inverting amplifier circuit (not shown in the diagram), if the gain resistor is Rg'', the feedback resistor is Rf'', and β'' = Rg'' / (Rg''+Rf''), and G'' is the absolute value of the amplifier's gain at the given frequency U'', then the gain G of the non-inverting amplifier circuit is given by equation (9).

[0092]

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[0093] When G'' is sufficiently greater than 1 (especially when β'' is large), G ≈ 1 + Rf'' / Rg''. A larger β'' results in a wider bandwidth for the inverting amplifier circuit and also makes it less susceptible to variations and changes in G''.

[0094] In Figure 3(B), when one non-inverting amplifier circuit is added, the total gain G of the amplifier circuit U is given by equation (9) × equation (7).

[0095] Gain resistors Rg' and feedback resistors Rf' can be easily modified by making part or all of their resistance values ​​variable, which has the effect of easily changing the various parameters expressed by the aforementioned formulas. The same applies when using gain resistors Rg'' and feedback resistors Rf'' in a non-inverting amplifier circuit.

[0096] <2.2 Example of characteristics when the gain of the amplifier is limited> In the graphs in Figures 4(A) and 4(B), examples of characteristics are superimposed for the circuit in Figure 3(A) when the gain of amplifier U is limited to 20dB and 40dB, and for comparison, when amplifier U' is in an open loop.

[0097] Figures 4(A) and 4(B) show the circuit constants and other parameters that form the basis of the characteristics illustrated in the graphs, as shown in Figure 3(A).

[0098] The values ​​of each resistor were determined so that the right-hand side of equation (1) was 1.5kΩ and the input impedance of the inverting amplifier circuit (equation (8)) was 3kΩ, thereby making the input impedance Zin of the active inductor 1kΩ. (The parallel resistance of 1.5kΩ and 3kΩ = 1kΩ.) Rg' and Rf' were selected considering equation (7) so that the DC gain of the amplifier circuit U was 20dB and 40dB, respectively. When the comparison amplifier U' was open-looped, Rf was set to 1.001MΩ so that the right-hand side of equation (1) was 1kΩ, and Rf' was omitted (infinite resistance).

[0099] The graph in Figure 4(A) shows an example of the frequency characteristics of the gain. The gain at 100 Hz is well close to 20 dB and 40 dB, and it can be seen that when the comparison amplifier U', shown by the dashed line, is open-loop, the gain is 60 dB. Furthermore, even when gain limiting is applied, the single gain frequency f T' can be seen to be 10MHz. (Strictly speaking, in an inverting amplifier circuit with gain limiting, as the gain decreases, the single gain frequency f T (Although there is a slight decrease, it is barely visible on the graph, so a detailed explanation is omitted.)

[0100] The graph in Figure 4(B) shows an example of the frequency characteristics of the input impedance.

[0101] The input impedance at frequencies well below the cutoff frequency fc' is 1kΩ in all cases. Single gain frequency f T At frequencies higher than ', when the DC gain is 20 dB and 40 dB, the input impedance Zin asymptotically approaches the value of (Rg' and Rf' in series) and (Rf) in parallel. This is the single-gain frequency f T At frequencies higher than ', U' ceases to perform its amplification function, resulting in a state similar to connecting -Vin and Vout with a resistor circuit consisting of (Rg' and Rf' in series) and (Rf) in parallel. When the comparison amplifier U' is in an open loop, the single gain frequency f is the same as in Figure 2(B). T At frequencies higher than ', the input impedance Zin asymptotically approaches the resistance of Rf.

[0102] <2.3 Regarding the plateau in Zin> In the examples described later, the input impedance Zin often asymptotically approaches a resistance value even lower than that at the gain limit. When this becomes a problem, the following methods (1) to (4) can be used to address the plateauing of Zin. (1) In the examples described later, the resistance value that the input impedance Zin asymptotically approaches will never be lower than Rg'. In other words, by selecting a resistance value that increases Rg', it is possible to asymptotically approach a higher resistance value. (For example, in the examples in Figures 4(A) and 4(B), the right-hand side of equation (1) is 1.5kΩ, the input impedance of the inverting amplifier circuit is 3kΩ, and these are selected so that their parallel connection is 1kΩ, resulting in Rg' being slightly less than 3kΩ. For example, if the right-hand side of equation (1) is 1.01kΩ and the input impedance of the inverting amplifier circuit is 101kΩ, Rg' can be increased to slightly less than 101kΩ, allowing it to asymptotically approach a higher resistance value.) (2) By adding the amplification element in parentheses on the left side of Figure 3(B), the effects of Rg' etc. can be eliminated, making it possible to asymptotically approach even higher resistance values. (3) Also, as can be seen from equation (2), the DC gain G when gain limiting is applied. DC A larger value is preferable because it increases the ratio of the DC resistance R to the feedback resistance Rf. If necessary, the DC gain G when the gain is limited can be adjusted. DC It is also possible to increase the gain beyond the required level and then attenuate it using an attenuator or similar device. (4) Furthermore, if necessary, an inductor can be added between the input -Vin and the input of the active inductor, or an inductor can be added in series with the feedback resistor Rf. However, in this case, if an inductor smaller than the ideal inductance (the inductance of the inductor L in the equivalent circuit) is used, the impedance will rise again at higher frequencies after Zin asymptotically approaches a certain resistance value.

[0103] Since all of these countermeasures for the capping of Zin (1) to (4) are also applicable to other examples besides gain limiting, we will now show examples where no countermeasures for the capping of Zin are taken.

[0104] As described in detail above, the active inductor in this embodiment is an inverting amplifier circuit in which the main amplifier is equipped with a gain resistor (Rg') and a second feedback resistor (Rf') to limit the gain.

[0105] Furthermore, in the active inductor of the present invention, an amplification element can be added between the input of the active inductor and the input of the main amplifier.

[0106] Furthermore, the active inductor of the present invention allows for the addition of an amplification element between the output of the main amplifier and the output of the active inductor.

[0107] (Third Embodiment) <3. Amplifier Bandwidth Limiting> <3.1 Overview of Amplifier Bandwidth Limiting> In the active inductor of the present invention, in order to achieve a larger inductance, from equation (6), the value of the feedback resistance Rf can be increased, or the single gain frequency f T It becomes clear that we should lower it.

[0108] Here, by using an inverting integrator circuit with a gain resistor Rg', a feedback capacitor Cf', and an amplifier U' as the amplifier U in Figure 1(A), a lower single gain frequency f can be achieved. T An example of this is shown. In this invention, this method will be referred to as "bandwidth limiting."

[0109] Figure 5 shows an example of a circuit with bandwidth limited by an inverting integrator.

[0110] In the inverting integrator circuit shown in Figure 5, when a sufficiently large bandwidth limit is applied (single gain frequency f due to bandwidth limiting) T (When ' is sufficiently reduced), the single gain frequency f when band-limited T ' is given by equation (10). (If the bandwidth limit is not large enough, the single gain frequency f is lower than that given by equation (10). T 'It will become.'

[0111]

number

[0112] The cutoff frequency fc' at this time is f T to f T This can be determined by equation (4) with the substitution '. Also, the inductance L at this time is f T to f T This can be determined by equations (5) and (6) after substituting '.

[0113] Single gain frequency f of amplifier U' T Generally, amplifiers have problems such as large variations between devices and susceptibility to temperature changes. In contrast, variations in resistors Rg' and capacitances Cf', and their effects on temperature changes, are generally much smaller than those of amplifiers U'. Therefore, the larger the bandwidth limit, the greater the f T ' is f T This has the effect of making it less susceptible to variations and changes.

[0114] Generally, it is not possible to add a feedback capacitor Cf' to a current-feedback operational amplifier. However, in some cases, it is possible to limit the bandwidth of a current-feedback operational amplifier by connecting a feedback resistor Rf' instead of a feedback capacitor Cf' and increasing its resistance value.

[0115] The feedback capacitance Cf' can be partially varied by using a variable capacitance element, which has the effect of changing the amount of bandwidth limiting. (The variation of the feedback resistor Rf and gain resistor Rg' is as described above.)

[0116] <3.2 Examples of characteristics when the amplifier's bandwidth is limited> In the graphs in Figures 6(A) and 6(B), in the circuit of Figure 5, with approximately 10 times the bandwidth limiting (f) compared to the case without bandwidth limiting for comparison (no Cf' = open loop, shown as a dashed line for comparison), the bandwidth limiting (f) is approximately 10 times greater. T 'ga f T The following shows an example of the characteristics when bandwidth limitations are applied at 1 / 10, approximately 100 times, and approximately 1000 times, superimposed on each other.

[0117] Figures 6(A) and 6(B) show the circuit constants and other parameters that form the basis of the characteristics illustrated in the graphs, as shown in Figure 5.

[0118] Gain resistance Rf was set to 1.001 MΩ and gain resistance Rg' to 3 kΩ as examples. No Cf was used for comparison (0 pF, no bandwidth limiting, f T For '=10MHz), a 10x bandwidth limit (f T '=1MHz), 100x bandwidth limit (f T '=100kHz), 1000x bandwidth limit (f T Each Cf was determined so that '=10kHz'.

[0119] Figure 6(A) shows an example of the frequency characteristics of the gain. When there is no bandwidth limiting (dashed line), the single gain frequency f T It can be seen that ' is 10MHz. Also, when bandwidth limiting is applied, f T ' is each, f T '=1MHz, 100kHz, 10kHz.

[0120] The graph in Figure 6(B) shows an example of the frequency characteristics of the input impedance. Below 100 Hz, the input impedance Zin asymptotically approaches 1 kΩ (1 / 1001 of 1.001 MΩ), as shown in equation (1).

[0121] When band-limited, at frequencies higher than the cutoff frequency fc', the input impedance Zin increases by 20 dB / decade, but asymptotically approaches approximately 3 kΩ. This is because at frequencies higher than the cutoff frequency fc', the impedance of the feedback capacitance Cf' decreases, causing Zin' to asymptotically approach Rg', resulting in a state similar to connecting -Vin and Vout with a resistor circuit consisting of Rg' and Rf in parallel. For comparison, when amplifier U' is in an open loop (dashed line), there is no feedback capacitance Cf', so, as in Figure 2(B), the single gain frequency f T At frequencies higher than ', the input impedance Zin asymptotically approaches the resistance of Rf.

[0122] Single gain frequency fT At frequencies higher than ', Zin' under gain limiting is Rg'+Rf', whereas Zin' under band limiting becomes Rg'. Therefore, the single gain frequency f when band limiting is applied. T At frequencies higher than ', Zin is lower than when gain limiting is applied. Therefore, when bandwidth limiting is applied, it is often more effective to add an amplification element (non-inverting) not shown in the diagram to the input side.

[0123] As described in detail above, the active inductor in this embodiment is an inverting integrating circuit in which the main amplifier has a gain resistor (Rg') and a feedback capacitance (Cf') to limit the bandwidth.

[0124] (Fourth Embodiment) <4. Combined Use of Gain Limitation and Bandwidth Limitation> <4.1 Overview of the combined use of gain limiting and bandwidth limiting> In the active inductor of the present invention, the aforementioned gain limiting and bandwidth limiting can be used in combination.

[0125] Figure 7 shows an example of a circuit that combines gain limiting and bandwidth limiting using a circuit configuration equivalent to an inverting imperfect integrator. Similar to gain limiting, gain limiting is performed using a gain resistor Rg' and a feedback resistor Rf', and similar to bandwidth limiting, bandwidth limiting is performed by connecting a feedback capacitor Cf' between the output of amplifier U' and the inverting input.

[0126] <4.2 Examples of characteristics when gain limiting and bandwidth limiting are used in combination> In the graphs of Figures 8(A) and 8(B), the following gain limiting and bandwidth limiting are applied to the circuit in Figure 7, and the 12 different results are superimposed.

[0127] Gain limiting: There are three types: amplifier U' is open-loop (no Rf', open-loop gain: 60dB), gain is limited to 40dB, and gain is limited to 20dB.

[0128] Bandwidth limitation: Amplifier U' has no bandwidth limitation (no Cf', f T (shown as a dashed line for comparison), approximately 10 times bandwidth limitation (fT 'ga f T There are four types: 1 / 10 of the original, approximately 100 times, and approximately 1000 times.

[0129] The circuit constants shown in Figure 7, which form the basis of the characteristics illustrated in the graphs of Figures 8(A) and 8(B), are almost the same as those for the gain limit and bandwidth limit described above, so their explanation will be omitted.

[0130] The graph in Figure 8(A) shows an example of the frequency characteristics of gain. This graph demonstrates that gain limiting and bandwidth limiting can be used in combination.

[0131] The graph in Figure 8(B) shows an example of the frequency characteristics of the input impedance. The three values ​​with higher input impedances in the high-frequency region represent data without band-limiting, and the results are similar to those in Figure 4(B). All other data represent data with band-limiting applied. At frequencies higher than the cutoff frequency fc', the input impedance Zin increases by 20 dB / decade, but at even higher frequencies, it asymptotically approaches the resistance value of Rg' and Rf connected in parallel. This is because the impedance of Cf' decreases at higher frequencies, causing Zin to approach the value of Rg' and Rf connected in parallel. (Similar to the band-limiting described above.)

[0132] As described in detail above, the active inductor of this embodiment is an inverting type incomplete integrating circuit in which the main amplifier is equipped with a gain resistor (Rg'), a second feedback resistor (Rf'), and a feedback capacitance (Cf') to limit the gain and bandwidth.

[0133] (Fifth Embodiment) <5. Another Bandwidth Limitation for the Amplifier> <5.1 Overview of other band-limiting methods for amplifiers> Here, resistor R LPF and capacity C LPF Here is another example of bandwidth limiting using a first-order RC low-pass filter (20 dB / decade).

[0134] Figure 9 shows an example of a circuit with a different type of bandwidth limiting.

[0135] If the bandwidth of the inverting amplifier circuit by amplifier U' is sufficiently wider than the desired bandwidth, the frequency response of the gain of the inverting amplifier circuit by amplifier U' near the desired bandwidth will be sufficiently flat. At such a flat frequency response, the resistor R LPF and capacity C LPF If bandwidth is limited by an RC low-pass filter (see Figure 9), the bandwidth is determined by the RC low-pass filter.

[0136] A rough guideline for the frequency response that can be considered nearly flat is that it is less than the cutoff frequency fc' of the amplifier U', and less than the cutoff frequency fc' of the RC low-pass filter. LPF Furthermore, it needs to be lower by the amount of the gain of the inverting amplifier circuit by amplifier U'. As shown in equation (4), the cutoff frequency fc' of the inverting amplifier circuit is the single gain frequency f T ' is 1 / gain of and similarly the cutoff frequency fc of a first-order RC low-pass filter. LPF The single gain frequency f TLPF It is 1 / gain of the frequency response. TLPF This is because if the value is not low enough, the attenuation rate of the RC low-pass filter will be greater than 20 dB / decade.

[0137] In other words, the cutoff frequency fc of a first-order RC low-pass filter LPF The single gain frequency f of amplifier U' is T The gain must be less than 1 / square of the gain. (In reality, the gain attenuates by approximately -3.01 dB at the cutoff frequency fc' of amplifier U', so it is not perfectly flat. This effect will be shown in the characteristic example described later.)

[0138] The load connected to the feedback resistor Rf and Vout is the resistor R LPF If the impedance is sufficiently higher than that, the amplification element shown in parentheses in Figure 9 is unnecessary. However, resistor R LPFIf the impedance is not sufficiently high, the load connected to the feedback resistor Rf or Vout can be added, for example, to prevent it from being affected by the load.

[0139] Furthermore, by adding this amplification element, the input impedance Zin can be varied by Rf, and R LPF (or C LPF ) allows the inductance of the equivalent inductor L to be varied, and also provides the effect that these can be varied independently. (In contrast, when this amplification element is absent, R LPF Changing this changes not only the inductance of the equivalent inductor L, but also the input impedance Zin. This is because, in this other band limit, when there is no amplification element, R is in series with Rf between the input -Vin and the output of U'. LPF Since it is also connected, Rf in equation (1) and equation (2) is (Rf + R LPF This is because the value replaced with ) will be applied. The resistor R shown in Figure 9 LPF and capacity C LPF The cutoff frequency fc of an RC low-pass filter using LPF This is expressed as in equation (11).

[0140]

number

[0141] <5.2 Example of characteristics when the amplifier has a different bandwidth limiting mechanism> In the graphs of Figures 10(A) and 10(B), both graphs superimpose 12 different characteristics when using an amplification element with a gain of 1 (G=+1) in the circuit of Figure 9, and applying different band-limiting with the following gains. Due to the wide frequency range, the frequency on the horizontal axis is expressed exponentially, from 1E-2=0.01Hz to 1E+8=100MHz.

[0142] When the loop is open (no Rf', open-loop gain: 60dB), the cutoff frequency fc of the first-order RC low-pass filter is... LPFare 10 Hz, 1 Hz, and 0.1 Hz. When the gain is limited to 40 dB, fc LPF are 1 kHz, 100 Hz, and 10 Hz. When the gain is limited to 20 dB, fc LPF are 100 kHz, 10 kHz, and 1 kHz. At each gain, the case without an RC low-pass filter is shown as a dashed line for comparison.

[0143] When the amplifier U’ is open-loop (gain is 60 dB: 1000 times), the single-gain frequency f T ’ is 10 MHz, and its cut-off frequency fc’ is 1 / 1000 of f T ’, which is 10 kHz. So, the cut-off frequency fc LPF of the first-order RC low-pass filter has an upper limit of 1 / 1000 of that, which is 10 Hz. When the gain is limited to 40 dB (100 times), fc’ is 1 / 100 of f T ’, which is 100 kHz. So, fc LPF has an upper limit of 1 / 100 of that, which is 1 kHz. When the gain is limited to 20 dB (10 times), fc’ is 1 / 10 of f T ’, which is 1 MHz. So, fc LPF has an upper limit of 1 / 10 of that, which is 100 kHz.

[0144] The circuit constants of FIG. 9 other than the RC low-pass filter are the same as the aforementioned gain limitations and are thus omitted.

[0145] The graph in FIG. 10(A) shows an example of the frequency characteristics of the gain.

[0146] It can be seen that the three solid-line data with a gain of 60 dB have cut-off frequencies as per the RC low-pass filter. However, for the data where fc LPF is 10 Hz, at frequencies above several kHz, the slope gradually becomes greater than 20 dB / decade. This is due to the fact that in the data where the cut-off frequency fc’ shown by the dashed line is 10 kHz, the gain gradually decreases above several kHz. For even lower fc LPF of 1 Hz and 0.1 Hz, this tendency is not discernible from the graph.

[0147] Gain of 40dB and fc LPF For 1kHz data, or with a gain of 20dB, fc LPF While the slope is similarly steep for the 100kHz data, this trend is not discernible from the graphs for the other values.

[0148] The graph in Figure 10(B) shows an example of the frequency characteristics of the input impedance.

[0149] When U' is open-loop (gain: 60dB, no Rf'), at low frequencies it asymptotically approaches 1kΩ as intended by Zin, but the single gain frequency f of the RC low-pass filter TLPF At frequencies higher than this, Rf asymptotically approaches 1001kΩ. LPF However, in the 10Hz data, a peak in input impedance occurs around 10kHz. LPF However, in the 1Hz data, a slight peak in input impedance is observed around 1kHz, but fc LPF However, with 0.1Hz data, the peak cannot be read from the graph.

[0150] When the gain is 40dB, at low frequencies, Zin asymptotically approaches 1kΩ as intended, but fc LPF Beyond a certain frequency, the value asymptotically approaches Rg' (approximately 3kΩ), and beyond 100kHz, it asymptotically approaches approximately 100kΩ. (This 100kΩ is the value obtained by connecting (Rg' and Rf' in series) and (Rf) in parallel.)

[0151] When the gain is 20dB, at low frequencies, Zin asymptotically approaches 1kΩ as intended, but fc LPF Beyond a certain frequency, it asymptotically approaches Rg' (approximately 3kΩ), and beyond 1MHz, it asymptotically approaches approximately 10kΩ. (This 10kΩ is also the value obtained by combining (Rg' and Rf' in series) and (Rf) in parallel.)

[0152] Furthermore, by adding an amplification element (non-inverting) not shown in the diagram between the inverting input of U' and the resistor Rg', the input impedance Zin' can be increased, resulting in a simple frequency response of input impedance Zin, similar to when U' is open-loop, which is often preferable.

[0153] The following application examples illustrate circuits that include the aforementioned bandwidth limitation, but it is also possible to apply other types of bandwidth limitation.

[0154] As described in detail above, the active inductor of this embodiment has an RC low-pass filter (R) between the output of the main amplifier and the output of the active inductor. LPF , C LPF ) is equipped to limit the bandwidth, and the single gain frequency (f) of the active inductor is limited. T ) is lower than the cutoff frequency (fc) of the main amplifier.

[0155] (Sixth Embodiment) <6. Application to Filters> <6.1 Overview of Applications to Filters> This section describes the application of the active inductor of the present invention to filters.

[0156] Figures 11(A) to 11(C) show the equivalent circuits of an LR low-pass filter, a CLR band-pass filter, and a CR high-pass filter. Figures 12(A) to 12(C) show examples of a low-pass filter using an active inductor, an example of a band-pass filter using an active inductor, and an example of a CR high-pass filter equipped with an amplifier. The dashed-dotted boxes in Figures 11(A) and 11(B) represent the portion corresponding to the active inductor of the present invention, and the dashed-dotted boxes in Figures 12(A) and 12(B) represent the active inductor of the present invention.

[0157] Figure 11(A) shows the equivalent circuit of the active inductor of the present invention. This circuit consists of an LR low-pass filter with an inductor L and a resistor R, and an amplification element with a negative gain factor, and operates as a first-order low-pass filter as a whole. Figure 11(A) is the same as Figure 1(B). The fact that the equivalent circuit of the active inductor of the present invention operates as a low-pass filter is also clear from the gain frequency characteristic graph mentioned above.

[0158] Figure 11(B) shows an example of a circuit in which a capacitance C is added to the input side of the equivalent circuit of the basic circuit of the active inductor of the present invention. The LR low-pass filter can also be used as a CLR band-pass filter by adding a capacitance C to the input. (The frequency characteristics will be described later.) The resistor Rd added to the input in parentheses is a damping resistor and is not an essential component. (The order of C and Rd may be reversed. The characteristics when Rd is included will be described later.)

[0159] Figure 11(C) shows the equivalent circuit of a reference CR high-pass filter, which is used in combination with an LR low-pass filter, etc., in the application example of the composite amplifier described later.

[0160] Figure 12(A) shows an example circuit of the active inductor of the present invention, illustrating a circuit with gain limiting and bandwidth limiting, similar to Figure 7. The fact that the active inductor of the present invention operates as a low-pass filter is also evident from the aforementioned graph of the gain frequency characteristics.

[0161] Figure 12(B) shows an example of a circuit in which capacitance C is added to the input side of the active inductor circuit of the present invention. The active inductor of the present invention can also be used as a CLR bandpass filter by adding capacitance C to the input. (The frequency characteristics will be described later.) Resistor Rd is a damping resistor and is not an essential component. (The order of C and Rd may be reversed. The characteristics when Rd is included will be described later.)

[0162] Figure 12(C) shows a reference example of a CR high-pass filter circuit, which is used in conjunction with a low-pass filter using an active inductor, etc., in the application example of the composite amplifier described later.

[0163] <6.2 Examples of Bandpass Filter Characteristics> Examples of the characteristics of the CLR bandpass filter in Figure 11(B) are shown in Figures 13(A) and 13(B). Similarly, examples of the characteristics of the CLR bandpass filter in Figure 12(B) are shown in Figures 14(A) and 14(B).

[0164] The center frequency fo of a CLR bandpass filter can be expressed as shown in equation (12).

[0165]

number

[0166] In these characteristic examples, the resistor R was set to 10kΩ and the gain of the amplification element was set to -10 times. L and C were selected with three different Q (Quality Factor) values: 0.07071, 0.7071, and 7.071, so that fo = 1kHz.

[0167] In Figures 13(A), 13(B), 14(A), and 14(B), the widest bandwidth is achieved around fo with a Q value of 0.07071, and the intermediate bandwidth is also at Q value = 0.7071. The narrowest bandwidth is achieved with a Q value of 7.071. The solid line represents the characteristics without resistor Rd, and the dashed line represents the characteristics with resistor Rd set to 10kΩ. Resistor Rd suppresses the gain peak and input impedance dip near fo.

[0168] As mentioned above, the active inductor of the present invention differs from an equivalent circuit using an ideal element and an amplifying element in that the input impedance plateaus in the high-frequency range.

[0169] When the Q value is at its narrowest, 7.071, this effect suppresses the gain peak near fo in Figure 14(A) and the input impedance dip in Figure 14(B). (Compare Figures 13(A) and 14(A), and Figures 13(B) and 14(B).) The examples in Figures 14(A) and 14(B) correspond to the CLR bandpass filter circuit in Figure 11(B) when the resistance Rd is approximately 50kΩ.

[0170] On the other hand, when the Q value is 0.7071 or 0.07071, Figures 13(A) and 14(A) show almost identical gain frequency characteristics, and Figures 13(B) and 14(B) also show similar input impedance frequency characteristics.

[0171] The active inductor of the present invention can be used in a way that does not cause problems due to the effects of the input impedance plateauing in the high-frequency range, and this example will be shown in the application examples described later.

[0172] As described in detail above, the active inductor of the present invention can be used as a low-pass filter.

[0173] Furthermore, the configuration of the active inductor of the present invention, which further uses a capacitive element on the input side, can be used as a bandpass filter.

[0174] (7th Embodiment) <7. Application to a Composite Amplifier> <7.1 Overview of Applications to Composite Amplifiers> In measuring instruments, the signal input impedance and signal output impedance are generally set to 50Ω, and coaxial cables with a characteristic impedance Z0 of 50Ω are used to transmit signals. (As a typical example other than 50Ω, 75Ω is commonly used in wireless applications, but 300Ω is also sometimes used.)

[0175] This section demonstrates an example of implementing a measurement amplifier with input and output impedances of 50Ω as a composite amplifier consisting of a low-frequency DC amplifier and a high-frequency AC amplifier. (50Ω is just one example; the same method can be applied to impedances other than 50Ω.)

[0176] <7.2 Basic Configuration and Characteristics Examples for Application to Composite Amplifiers> Figure 15 shows an example of a basic equivalent circuit of such a composite amplifier, and Figures 16(A) and 16(B) show its frequency characteristics. Figure 17 shows a specific circuit example in which the active inductor of the present invention is applied to such a composite amplifier, and Figures 18(A) and 18(B) show its frequency characteristics.

[0177] In Figure 15, the area enclosed by the dashed line is the inductor L. L and capacity C H This shows a demultiplexer using an inductor L. L Output Vo L The load is 50Ω R L Therefore, the capacity C H Output Vo H The load is 50Ω R H In this case, the input impedance Zin of the demultiplexer can be expressed as in equation (13), and the L such that this becomes 50Ω L and C H I'll do that.

[0178]

number

[0179] Furthermore, in this demultiplexer, the frequency f0 at which the low-frequency side and the high-frequency side switch can be expressed as shown in equation (14).

[0180]

number

[0181] Low-frequency cutoff frequency fc Land the high-frequency cutoff frequency fc H These can be expressed as shown in equations (15) and (16), respectively, and fc L =fc H In that case, equation (13) is obtained.

[0182]

number

[0183]

number

[0184] In Figure 15, the gains of the low-frequency DC amplifier and the high-frequency amplifier are set to -G times (inverting amplifier circuit). (The high-frequency side can be either a DC amplifier or an AC amplifier.) The summing circuit consists of an summing element indicated by a + sign inside a circle and an inverting amplifier circuit with a gain of -G' times. The output impedance (Ro) of the summing circuit is 50Ω, and the load (R) connected to the output of the summing circuit is... LD The example also shows a 50Ω value. In this example, all examples are inverting amplifier circuits, but this is not the only option. The capacitance Co shown in parentheses at the output of the AC amplifier is an optional component for blocking the DC component in the signal, and should be provided only when necessary.

[0185] If it is sufficient to obtain separate outputs for the low-frequency and high-frequency sides, the adder can be omitted. Instead, a 50Ω resistor (not shown in the diagram) can be placed at the output of each of the amplification elements on the low-frequency and high-frequency sides to obtain the output.

[0186] Incidentally, an amplifier circuit with an input impedance of, for example, 50 Ω can also be used as a current amplifier whose input impedance is matched to 50 Ω. This is because the input current Iin is converted into an input voltage Vin (= Iin × Zin) by the input impedance Zin. That is, the active inductor of the present invention can also be used as a current amplifier that can easily vary the input impedance Zin, the inductance of the equivalent inductor L, the cut-off frequency fc, and the like.

[0187] FIG. 16(A) shows the frequency characteristics of the gain of the circuit of FIG. 15, and FIG. 16(B) shows the frequency characteristics of the input impedance of the circuit of FIG. 15. The characteristics on each of the high-frequency side and the low-frequency side (the characteristics when the other signal is not applied to the adder circuit) are shown by broken lines, and the characteristics of the entire composite amplifier are shown by solid lines.

[0188] The frequency f0 is set to 10 kHz, and the overall gain (-G × -G') is set to 200 times. Ro is also R LD Since Ro is also 50 Ω, the voltage appearing at Vout is half of the output voltage of the adder circuit, so the gain in FIG. 16(A) is 40 dB = 100 times. A flat gain frequency characteristic is obtained, and it can be seen that the high-frequency side and the low-frequency side are switched at 10 kHz.

[0189] In FIG. 16(B), a frequency characteristic of a flat input impedance of 50 Ω is obtained, and it can be seen that, as in FIG. 16(A), the high-frequency side and the low-frequency side are switched at 10 kHz.

[0190] <7.3 Specific Circuit of Composite Amplifier and Example of Its Characteristics> FIG. 17 shows an example in which a composite amplifier is realized by replacing the circuit of FIG. 15 with a specific circuit using the active inductor of the present invention, and FIGS. 18(A) and 18(B) show this example of characteristics.

[0191] Figure 18(A) shows an example of the frequency characteristics of the gain of the circuit in Figure 17, and Figure 18(B) shows an example of the frequency characteristics of the input impedance of the circuit in Figure 17.

[0192] The constants in the circuit shown in Figure 17 were selected to be essentially the same as those used in Figure 15. However, in the CR high-pass filter, the input impedance was made slightly higher than 50Ω while maintaining the same gain and cutoff frequency. (Details of this will be explained later.)

[0193] Low-frequency amplifier U L ' is DC gain G DC :100dB, single gain frequency f T The frequency is set to 10MHz. The high-frequency amplifier U H ' is DC gain G DC :100dB, single gain frequency f T The bandwidth is wider than the lower frequency side, at 100MHz. Amplifier U of the summing circuit S ' is DC gain G DC :80dB, single gain frequency f T :100MHz, which also has a wider bandwidth than the lower frequency side. L Gain and U of the amplification circuit H The gain of the amplification circuit by ' is set to -100 times for both, U S The gain of the summing circuit was set to -2 times.

[0194] In Figures 18(A) and 18(B), the characteristics of the high-frequency side and the low-frequency side (characteristics when the other signal is not applied to the summing circuit) are shown by dashed lines, and the characteristics of the entire composite amplifier are shown by a solid line.

[0195] In Figure 18(A), a frequency response with a flat gain, similar to that in Figure 16(A), is obtained, but at 1 MHz, it is approximately -3 dB. This is due to the high-frequency amplifier U. H Since it is used with a gain of -100x, the cutoff frequency is the single gain frequency f T This is because it is approximately 1 MHz, which is about 1 / 100th of 100 MHz. (High-frequency amplifier U) H'Use a wider bandwidth amplifier or change the gain distribution U L 'side and U H Lower the gain on the side U S Increasing the gain on the 'side' side will result in a flatter gain frequency response.

[0196] Figure 18(B) shows that a flat frequency response with a constant input impedance of 50Ω is obtained, similar to Figure 16(B). The impedance on the low-frequency side when using the active inductor of the present invention asymptotically approaches a constant value of several hundred ohms as the frequency increases, but this is compensated for by making the impedance on the high-frequency side slightly higher than 50Ω, resulting in a flat frequency response with a constant input impedance of 50Ω overall.

[0197] <7.4 Modification of a composite amplifier - 1> In Figure 17, the high-frequency amplifier U H This shows an example where an operational amplifier is assumed to be used as '. As a variation of this, U H Let's consider the case where a high-frequency amplifier, such as those used in wireless communication, is used.

[0198] In such high-frequency amplifiers, the input impedance is often matched to 50Ω, but it can be other values. For example, if it is 75Ω, it can be made to 50Ω by connecting a 150Ω resistor in parallel with the input. Alternatively, the input impedance can be made to 50Ω by connecting a feedback resistor Rf as shown in Figure 1 and applying equation (1).

[0199] Furthermore, when using a high-frequency amplifier, an operational amplifier U as shown in Figure 17 can be used. S In summing circuits using ', insufficient bandwidth may occur. In such cases, a high-frequency power combiner can be used instead of the summing circuit. There are various circuit designs for power combiners, but if necessary, you should select one that can also be used with DC.

[0200] <7.5 Modification of a composite amplifier - 2> Figures 15 and 17 show examples where the entire low-frequency inductance is borne by the active inductor of the present invention. The low-frequency input side (Vin and L in Figure 15) L Between Vin and (Rg L 'and Rf L It is also possible to connect an inductor (not shown in the diagram) between the connection points and have that inductor bear a portion of the low-frequency inductance.

[0201] Such modifications are applicable to all applications of the active inductor of the present invention, including the aforementioned application to filters and the application to composite amplifiers described later.

[0202] As described in detail above, the composite amplifier of this embodiment comprises a low-pass filter using the active inductor of the present invention, a CR high-pass filter, and a high-pass filter using a second main amplifier.

[0203] (Eighth Embodiment) <8. Application to Multi-Amplifier Circuits for Audio> <8.1 Overview of Applications to Multi-Amplifier Circuits for Audio> In this example, we assume a multi-amplifier circuit for audio applications as shown below.

[0204] This audio multi-amplifier circuit drives a 3-way speaker system consisting of a tweeter (high-frequency speaker), a midrange speaker (squawker), and a woofer (low-frequency speaker). Furthermore, it is a 3-way multi-amplifier circuit in which each of the high-frequency, midrange, and low-frequency speakers is driven by an independent power amplifier. (With a single amplifier, there is a possibility of being affected by back electromotive force from other speakers connected together. For example, back electromotive force from the woofer may affect the squawker and cause distortion.) Such a multi-amplifier circuit is also a type of composite amplifier.

[0205] The low-frequency amplifier and speaker are responsible for frequencies below 200 Hz, and the cut-off frequency of the low-pass filter is set to 200 Hz. The high-frequency amplifier and speaker are responsible for frequencies above 5 kHz, and the cut-off frequency of the high-pass filter is set to 5 kHz. The mid-frequency amplifier and speaker are responsible for 200 Hz to 5 kHz, and the overall frequency characteristics are to be made flat.

[0206] Volume controls for adjusting the volume of each frequency range, phase inversion switches of each power amplifier for adjusting the connection of sounds, etc. are omitted, and only the basic circuit is shown.

[0207] The gains of the amplifiers are each -10 times. When the input is 1 Vrms, the output is 10 Vrms, and 12.5 W can be supplied to an 8 Ω speaker respectively. In the audio field, low-impedance transmission / high-impedance reception is fundamental, so in this example, the input impedance Zin is set to a common 10 kΩ.

[0208] <8.2 Equivalent Circuit of Audio Multi-Amplifier Circuit and Its Characteristic Example> FIG. 19 shows an example of realizing an audio multi-amplifier circuit by combining the equivalent circuits of the three types of filters shown in FIGS. 11(A) to 11(C). The dashed-dotted line frame indicates the part to which the active inductor of the present invention can be applied, similar to FIGS. 11(A) and 11(B).

[0209] FIG. 20(A) shows an example of the frequency characteristics of the gain of the circuit in FIG. 19, and FIG. 20(B) shows an example of the frequency characteristics of the input impedance of the circuit in FIG. 19.

[0210] By selecting the constants of the circuit in FIG. 19 as follows, the frequency characteristics shown in FIGS. 20(A) and 20(B) were obtained.

[0211] L L and R L The cut-off frequency of the LR low-pass filter consisting of is set to 200 Hz. (L and R in Equation (3) are L L and RL (By substituting this, the circuit constants were calculated.)

[0212] C H and R H The cutoff frequency of the CR high-pass filter consisting of the above components is set to 5 kHz, and the circuit constants were calculated using equation (16) above.

[0213] Rd, C B , L B , R B The constants of the CLR bandpass filter were selected so that the overall gain frequency response is flat at 20 dB and the input impedance Zin frequency response is flat at 10 kΩ.

[0214] To make Zin 10kΩ, R L , R B , R H Each resistor was set to 10kΩ.

[0215] In Figure 20(A), the frequency characteristics of the gain of the LR low-pass filter and the CR high-pass filter are shown by dashed lines, the frequency characteristics of the gain of the CLR band-pass filter are shown by a dashed line, and the frequency characteristics of the combined gain are shown by a solid line. The cutoff frequency of the LR low-pass filter is 200 Hz, and the cutoff frequency of the CR high-pass filter is 5 kHz, and it can be seen that a flat frequency characteristic with a gain of 20 dB is obtained across all frequencies.

[0216] Similarly, in Figure 20(B), the frequency characteristics of the input impedance of the LR low-pass filter and the CR high-pass filter are shown by dashed lines, the frequency characteristics of the input impedance of the CLR band-pass filter are shown by a dashed line, and the frequency characteristics of the input impedance of Zin are shown by a solid line. The cutoff frequency of the LR low-pass filter is 200 Hz, and the cutoff frequency of the CR high-pass filter is 5 kHz, and it can be seen that a flat frequency characteristic of 10 kΩ input impedance is obtained at all frequencies.

[0217] <8.3 Specific Circuits and Characteristics Examples of Audio Amplifiers> Figure 21 shows an example of an audio multi-amplifier circuit realized by replacing the circuit in Figure 19 with a specific circuit using the active inductor of the present invention, and Figures 22(A) and 22(B) show examples of its characteristics. The dashed box in Figure 21 indicates the part to which the active inductor of the present invention is applied, and it is a circuit equivalent to the circuit in Figure 7.

[0218] Figure 22(A) shows an example of the frequency characteristics of the gain of the circuit in Figure 21, and Figure 22(B) shows an example of the frequency characteristics of the input impedance of the circuit in Figure 21.

[0219] The constants in the circuit shown in Figure 21 were selected to be essentially the same as those used in Figure 19. However, in the CR high-pass filter, the cutoff frequency was kept at the same 5kHz, while the input impedance was made higher than 10kΩ. (Details of this will be explained later.)

[0220] Figure 22(A) shows the frequency characteristics of the gain of the low-pass filter and CR high-pass filter using an active inductor as dashed lines, the frequency characteristics of the gain of the band-pass filter using an active inductor as a dashed line, and the frequency characteristics of the combined gain of these as a solid line. It can be seen that a flat gain frequency characteristic similar to that of Figure 20(A) has been obtained.

[0221] Similarly, in Figure 22(B), the frequency characteristics of the input impedance of the low-pass filter and CR high-pass filter using an active inductor are shown by dashed lines, the frequency characteristics of the input impedance of the band-pass filter using an active inductor are shown by a dashed line, and the frequency characteristics of the input impedance of Zin are shown by a solid line.

[0222] The input impedance of the low-pass filter using the active inductor of the present invention increases with frequency, Rg L 'and Rf LIt asymptotically approaches the parallel resistance value. (This is similar to Figure 8(B), which shows the frequency characteristics of the input impedance of the circuit in Figure 7.) Furthermore, in the bandpass filter using the active inductor of the present invention, as the frequency increases, Rg B 'and Rf B It asymptotically approaches the sum of the parallel resistance value of and the resistance value of Rd.

[0223] On the other hand, the input impedance of the CR high-pass filter exhibits a flat frequency response above the cutoff frequency. Therefore, by setting the parallel value of the input impedances of the low-pass filter using an active inductor, the band-pass filter using an active inductor, and the CR high-pass filter to a predetermined 10kΩ in the high-frequency region, a flat frequency response of the input impedance of Zin as shown in Figure 22(B) can be obtained.

[0224] The active inductor of the present invention differs from an equivalent circuit using ideal elements and amplification elements in that the input impedance plateaus in the high-frequency range. However, in this example, it can be used in combination with a high-pass filter as a low-pass filter or band-pass filter, resulting in a flat frequency response with a Zin of 10kΩ across all frequencies, similar to Figure 20(B). In this example, one band-pass filter is used, but it is also possible to divide the frequency into four (4-way) sections using two band-pass filters, and it is also possible to increase the number of frequency divisions by using multiple band-pass filters. A composite amplifier using multiple such band-pass filters is also included in the present invention.

[0225] As described in detail above, the composite amplifier of this embodiment comprises a low-pass filter using the active inductor of the present invention, a band-pass filter using the active inductor of the present invention further equipped with a capacitive element on the input side, and a CR high-pass filter and a high-pass filter using a second main amplifier. [Explanation of Symbols]

[0226] Rf First feedback resistor Rg' gain resistance Rf' Second feedback resistor Cf' Feedback capacitance R LPF Resistor of RC low-pass filter C LPF Capacitance of RC low-pass filter f T Single Gain Frequency of Active Inductor fc Main amplifier cutoff frequency

Claims

1. This configuration involves connecting a first feedback resistor (Rf) between the output of the main amplifier and the inverting input. The inverting input of the main amplifier is used as the input, and the output of the main amplifier is used as the output. An active inductor with voltage input and voltage output.

2. The active inductor according to claim 1, wherein the main amplifier is an inverting amplifier circuit that limits the gain by comprising a gain resistor (Rg') and a second feedback resistor (Rf').

3. The active inductor according to claim 1, wherein the main amplifier is an inverting integrating circuit with a gain resistor (Rg') and a feedback capacitance (Cf') to limit the bandwidth.

4. The active inductor according to claim 1, wherein the main amplifier is an inverting imperfect integrating circuit that limits the gain and bandwidth by comprising a gain resistor (Rg'), a second feedback resistor (Rf'), and a feedback capacitance (Cf').

5. An RC low-pass filter (R) is placed between the output of the main amplifier and the output of the active inductor. ＬＰＦ , C ＬＰＦ ) and limit the bandwidth, The single gain frequency (f) of the active inductor. Ｔ The active inductor according to claim 1, wherein the frequency (fc) is lower than the cutoff frequency (fc) of the main amplifier.

6. The active inductor according to any one of claims 1 to 5, wherein an amplification element is added between the input of the active inductor and the input of the main amplifier.

7. The active inductor according to any one of claims 1 to 5, wherein an amplification element is added between the output of the main amplifier and the output of the active inductor.

8. A low-pass filter using an active inductor according to any one of claims 1 to 5.

9. A bandpass filter using an active inductor according to any one of claims 1 to 5, further comprising a capacitive element on the input side.

10. A low-pass filter using an active inductor according to any one of claims 1 to 5, A CR high-pass filter and a high-pass filter using a second main amplifier, A composite amplifier equipped with the following features.

11. A low-pass filter using an active inductor according to any one of claims 1 to 5, A bandpass filter using an active inductor according to any one of claims 1 to 5, further comprising a capacitive element on the input side, A CR high-pass filter and a high-pass filter using a second main amplifier, A composite amplifier equipped with the following features.

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