Multi-stage amplification circuit

Abstract

A multistage amplifier circuit (1) includes multiple amplifier circuits (2) that are connected in series and encompass a 0 dB frequency at which the size of a normalized transfer function normalized to a low-frequency gain becomes 1 in response to a frequency other than a direct current frequency.

Description

Technical Field

[0001] The present invention relates to an amplifier circuit for amplifying a baseband signal.

Background Art

[0002] In the communication of electrical signals and optical signals, codes such as NRZ (Non Return to Zero) and PAM4 (4-Level Pulse Amplitude Modulation), which are baseband signals, are used (see Non-Patent Document 1). Communication using these codes has the advantages of a simple configuration of the transmission and reception circuit and low latency.

[0003] In both the case of electrical signals and optical signals, signal processing for signal amplification is performed on the receiving side. When the attenuation of the signal in the communication path is large, the signal amplitude becomes small, so it is necessary to increase the gain of signal amplification. When increasing the gain, a configuration is adopted in which amplifier circuits for baseband signals are connected in series in several stages.

[0004] However, when N amplifier circuits are connected in series, the 3 dB bandwidth f -3dB of one amplifier circuit becomes narrower than the bandwidth f_N, and f_N = f -3dB (2 1 / N -1) 0.5 There was a problem that this would happen (see Non-Patent Document 2).

Prior Art Documents

Non-Patent Documents

[0005]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0006] An object of the present invention is to provide a multistage amplifier circuit capable of suppressing a decrease in bandwidth and increasing gain as compared with a single-stage amplifier circuit.

Means for Solving the Problems

[0007] The multistage amplifier circuit of the present invention is characterized in that a plurality of amplifier circuits in which the magnitude of the normalized transfer function normalized by the low-frequency gain becomes 1 at frequencies other than DC, i.e., 0 dB frequencies, are connected in series. Comprising a configuration, when each stage of the amplifier circuit is represented by a circuit model, it includes an input capacitance connected between the signal input terminal and the ground, an amplification section configured to amplify the signal input to the signal input terminal, an output resistance with one end connected to the output terminal of the amplification section, an output capacitance connected between the other end of the output resistance and the ground, and an inductor with one end connected to the other end of the output resistance and the other end connected to the signal output terminal. It is characterized by the above.

[0008] Also , in one configuration example of the multistage amplifier circuit of the present invention, the output resistance is R o , the output capacitance is C o , the inductor is L, and the input capacitance of the next-stage circuit connected to each stage of the amplifier circuit is C nx , when Q = (L / C nx ) 1 / 2 / R o , k c = C o / C nx , when Q and k c , the range of Q and k 4 is max[(7 / 32){1 - 2(27 / 28) c +(16 / 7)(k 2 - 0.5)}, c √{4k c (1 - k c )}-1] ≦ (Q - 1) ≦ {0.5 - 12(k 2 - 0.5)c -0.5) 3 It is represented by} / 8. Also, one configuration example of the multi-stage amplifier circuit of the present invention is characterized in that when the 0 dB frequencies of the amplifier circuits of each stage are different, the average of the 0 dB frequencies of the amplifier circuits of each stage is F1. Also, one configuration example of the multi-stage amplifier circuit of the present invention is characterized in that when the resonance sharpness of the amplifier circuits of each stage is different, the average of the resonance sharpness of the amplifier circuits of each stage is the above Q.

[0009] Also, the multi-stage amplifier circuit of the present invention It has a configuration in which a plurality of amplifier circuits, each having a 0 dB frequency at which the magnitude of the normalized transfer function normalized by the low-frequency gain becomes 1 at frequencies other than DC, are connected in series. When the configuration of each stage amplifier circuit is represented by a circuit model, it includes a first amplifier circuit and a second amplifier circuit connected to the subsequent stage of the first amplifier circuit. The first amplifier circuit includes a first input capacitance connected between a signal input terminal and ground, a first amplifier section configured to amplify a signal input to the signal input terminal, a first output resistance with one end connected to the output terminal of the first amplifier section, a first output capacitance connected between the other end of the first output resistance and ground, and a first inductor with one end connected to the other end of the first output resistance. The second amplifier circuit includes a second input capacitance connected between the other end of the first inductor and ground, a second amplifier section configured to amplify a signal input from the first amplifier circuit, a second output resistance with one end connected to the output terminal of the second amplifier section, a second inductor with one end connected to the other end of the second output resistance and the other end connected to a signal output terminal, and a second output capacitance connected between the signal output terminal and ground.

[0010] Also, one configuration example of the multi-stage amplifier circuit of the present invention is characterized in that the lower frequency of the 0 dB frequencies of the first amplifier circuit is equal to the 0 dB frequency of the second amplifier circuit, and the product of the extreme value of the magnitude of the normalized transfer function of the first amplifier circuit and the extreme value of the magnitude of the normalized transfer function of the second amplifier circuit at the lower frequency is 1. Also, in one configuration example of the multi-stage amplifier circuit of the present invention, the first output resistance is Ro , let the first output capacitance be C o , let the first inductor be L, and the second input capacitance be C nx , among the 0 dB frequencies of the first amplifier circuit, let the extreme value of the normalized transfer function of the first amplifier circuit at the lower frequency be |h(Ωa2)|, and Q = (L / C nx ) 1 / 2 / R o , k c = C o / C nx , when it is set as such, the ranges of Q and k c are represented by |h(Ωa2)| -2 =(2 + 3√3) / (3√3)+{4 / (3√3)}(k c - 1)-({(4 + 4√3) / 9}(Q - 1), 1 < |h(Ωa2)| -2 ≦1.82, 0.5 < k c ≦1.25.

Advantages of the Invention

[0011] According to the present invention, by connecting in series a plurality of amplifier circuits in which the magnitude of the normalized transfer function normalized by the low-frequency gain becomes 1 at frequencies other than direct current, the decrease in the bandwidth can be suppressed compared to the case of a single-stage amplifier circuit, and the gain can be increased compared to the case of a single-stage amplifier circuit.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

BEST MODE FOR CARRYING OUT THE INVENTION

[0013] [First Embodiment] Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a block diagram showing the configuration of a multi-stage amplifier circuit according to the first embodiment of the present invention. The multi-stage amplifier circuit 1 of this embodiment is formed by connecting a plurality of amplifier circuits 2 having a 0 dB frequency at which the magnitude of the transfer function normalized by the low-frequency gain becomes 1 at frequencies other than DC in series between the input terminal 3 and the output terminal 4.

[0014] Each amplification circuit 2 is composed of a circuit having an inductor for generating resonance, a capacitive input load, and a resistor for suppressing resonance. The circuit model of the amplification circuit 2 is shown in FIG. 2. The amplification circuit 2 is composed of a main circuit 200 and a resonance inductor L connected between the main circuit 200 and the input capacitance of the next stage. In FIG. 2, 5 is the signal input terminal of the amplification circuit 2, and 6 is the signal output terminal of the amplification circuit 2.

[0015] When the main circuit 200 is modeled, as shown in FIG. 2, an input capacitance C connected between the signal input terminal 5 and the ground i , an amplification unit 201 with a gain G that amplifies the signal input to the signal input terminal 5, and an output resistor R with one end connected to the output terminal of the amplification unit 201 o , and an output capacitance C connected between the other end of the output resistor R o and the ground. o It has a configuration including When the amplification circuit 2 is made multi-stage, as shown in FIG. 3, a load capacitance C is connected to the output of the amplification circuit 2 nx (the input capacitance C of the next-stage amplification circuit 2 i ).

[0016] Examples of the main circuit 200 include a CMOS inverter amplification circuit, a FET source-grounded circuit, a differential amplification circuit, etc. Also, at high frequencies, an emitter-grounded circuit can also be used as the main circuit 200. The main circuit 200 has a constant low-frequency gain G from near DC to the cutoff frequency on the high-frequency side. The transfer function of the amplification circuit 2 is expressed by the following equation (1).

[0017]

Equation

[0018] In equation (1), V i is the input voltage of the amplification circuit 2, and V o is the output voltage of the amplification circuit 2. By normalizing equation (1) with the gain G, a normalized transfer function h(ω) as shown in equation (2) is obtained.

[0019]

number

[0020] Normalized angular frequency Ω=ω(LC nx ) 1 / 2 , resonance sharpness Q=(L / C nx ) 1 / 2 / R o , output capacitance C o and the input capacitance C of the next stage nx Compared to c =C o / C nx Then, we obtain the following equation (3).

[0021]

number

[0022] From equation (3), the square of the normalized transfer function of amplifier circuit 2, |h(Ω)| 2 is expressed by the following equation (4).

[0023]

number

[0024] The normalized transfer function 0 dB frequency F1=Ω1 / 2π(F1>0) at which the magnitude of the normalized transfer function of the amplifier circuit 2 becomes 1, i.e., 0 dB, is |h(2πF1)| 2 =1 and is expressed by the following equation (5).

[0025]

number

[0026] The normalized transfer function 0 dB frequency F1 and frequency f are expressed as F1=f(LC nx ) 1 / 2 That is, the frequency f is expressed by the resonant inductor L and the input capacitance C of the next stage. nx The resonance frequency 1 / (LCnx ) 1 / 2 The normalized frequency normalized in this way is the 0 dB frequency F1 of the normalized transfer function. As an example, when k c = 0.5 and the value of Q is selected to suppress resonance, in the case of Q = 1, |h(2πF1)| = 1 at 2πF1 = 1, and the normalized transfer function of the amplifier circuit 2 becomes like the broken line 40 in FIG. 4.

[0027] Even when N stages (N is an integer of 2 or more) of the amplifier circuit 2 are connected as shown in FIG. 1, the magnitude of the normalized transfer function of the multi-stage amplifier circuit 1 at 2πF1 = 1 is |h(2πF1)| N = 1. On the other hand, when N stages of the amplifier circuit 2 are connected, the gain of the multi-stage amplifier circuit 1 is G N becomes. If G > 1, the gain increases by connecting the amplifier circuit 2 in multiple stages.

[0028] The normalized transfer function of the multi-stage amplifier circuit 1 when 4 stages of the amplifier circuit 2 are connected is shown by the solid line 41 in FIG. 4. Even when 4 stages of the amplifier circuit 2 are connected, |h(2πF1)| 4 remains 1 at 2πF1 = 1, and the decrease in the bandwidth up to 2πF1 = 1 can be suppressed. In a conventional multi-stage amplifier circuit, when 4 stages of an amplifier circuit with a bandwidth f0 are connected, the bandwidth is f0(2 1 / 4 - 1) 0.5 = 0.435f0, which is more than halved compared to the bandwidth f0 of a single-stage amplifier circuit. On the other hand, in the multi-stage amplifier circuit 1 of this embodiment, the decrease in the bandwidth can be suppressed to 20% or less.

[0029] In the multi-stage amplifier circuit 1 of this embodiment, if the amplification factor of each stage of the amplifier circuit 2 is 1 or more, the decrease in the band can be suppressed compared to the case of a single-stage amplifier circuit, and the gain can be increased. In the multi-stage amplifier circuit 1 of this embodiment, the gains G of the amplifier circuits 2 of each stage do not have to be the same.

[0030] In the above description, as an example, k c = 0.5 and Q = 1 were used, but k c = 0.7 and Q = 1 may also be used. k cWhen k = 0.7 and Q = 1, the normalized transfer function of the amplifier circuit 2 becomes like the dashed line 50 in Fig. 5. k c When k = 0.7, not only |h(2πF1)| = 1 at 2πF1 = 1, but there also exists a frequency at which |h(2πF1)| = 1 when 2πF1 > 1, k c Compared with the case of k = 0.5, it has a wider bandwidth.

[0031] k c The magnitude of the normalized transfer function of the multi - stage amplifier circuit 1 with four - stage connection of the amplifier circuit 2 when k = 0.7 and Q = 1 is shown by the solid line 51 in Fig. 5. k c When k = 0.7 and Q = 1, k c Compared with the characteristics of the multi - stage amplifier circuit 1 with four - stage connection of the amplifier circuit 2 when k = 0.5 and Q = 1 (the solid line 41 in Fig. 4), the ripple (the ratio of the maximum value to the minimum value) of the normalized transfer function becomes larger. Since a large ripple in the normalized transfer function causes distortion in the signal waveform, it is desirable that the ripple be smaller.

[0032] k and Q for making the ripple of the normalized transfer function be ±3 dB or less are obtained. To simplify the analysis, the extreme values of the reciprocal of Equation (4) (Ωa1) c and (Ωa2) 2 are obtained and are represented by the following equations (6) and (7). 2

[0033]

Equation

[0034]

Equation

[0035] |h(Ωa1)| becomes the maximum value and |h(Ωa2)| becomes the minimum value. When Q = 1 and k c is near 0.5, |h(Ωa1)| and |h(Ωa2)| are obtained by approximate analysis and numerical analysis and are represented by the following equations (8) and (9).

[0036] ​

Number

[0037]

Number

[0038] In the case of the multistage amplifier circuit 1 in which the amplifier circuit 2 is connected in four stages, for example, the fourth power of |h(Ωa1)| 2 should be 2 or less, and the fourth power of |h(Ωa2)| 2 should satisfy the condition of being 1 / 2 or more. From this condition, the following equations (10) and (11) are obtained.

[0039]

Number

[0040]

Number

[0041] Also, the condition that there exists a frequency at which the magnitude of the normalized transfer function of the amplifier circuit 2 becomes 0 dB, i.e., (2πF1) 2 is a real number means that in Equation (5), the last term in the numerator Q√(4k c 2 -4k c +Q 2 ) should be a real number. That is, the following equation (12) should hold.

[0042]

Number

[0043] From equations (10), (11), and (12), the ranges of Q and k c for which the ripple of the normalized transfer function in the multistage amplifier circuit 1 with the amplifier circuit 2 connected in four stages is ±3 dB or less are represented by the following equation (13). This range corresponds to the hatched portion 60 in FIG. 6. The vertical axis in FIG. 6 is Q - 1, and the horizontal axis is k c - 0.5.

[0044]

Number

[0045] With the above configuration, in the multi-stage amplifier circuit 1 of this embodiment, it is possible to suppress a decrease in the bandwidth and increase the gain as compared with the case of a single-stage amplifier circuit. As described above, in the multi-stage amplifier circuit 1 of this embodiment, the gains G of the amplifier circuits 2 in each stage do not have to be the same.

[0046] In FIG. 2, the output capacitance C of the main circuit 200 o alone is set to k c ≧0.5. However, if it is not possible to set k o ≧0.5 with only the inherent C of the main circuit 200 c , an additional capacitance C o ' may be connected in parallel with the output capacitance C as shown in FIG. 7. This additional capacitance C o ' may be a wiring capacitance. o ' may be a wiring capacitance.

[0047] In the above description, the normalized transfer function 0 dB frequencies at which the magnitude of the normalized transfer function becomes 0 dB are the same in all stages of the multi-stage amplifier circuit 1.

[0048] On the other hand, it is also possible that the normalized transfer function 0 dB frequencies are different in the amplifier circuits 2 in each stage, but are in the vicinity of F1 and the average of the normalized transfer function 0 dB frequencies of the amplifier circuits 2 in each stage is F1. In this case, the frequency is normalized by the average resonance frequency (LC nx ). -1 / 2 The normalized transfer function 0 dB frequency of the k-th stage amplifier circuit 2 is represented as F1 + δF k . When the magnitude of the normalized transfer function at this time is such that the normalized angular frequency Ω1 + δΩ k = F1 + δF k in the k-th stage, it is represented by the following equation (14).

[0049]

Number

[0050] From Equation (14), the normalized transfer function 0 dB frequency is Ω1 + δΩ k For the case of Ω1, the magnitude of the normalized transfer function at Ω1 is approximated by the first-order term of δΩ k to be expressed by the following Equation (15).

[0051]

Equation

[0052] Here, A1 is the coefficient of the first-order term of δΩ k and is independent of δΩ k and is a value that depends on Ω1, Q, k c The left side of Equation (15) represents the square of the magnitude of the normalized transfer function |h k (Ω1)| 2 The square of the magnitude of the overall normalized transfer function |H(Ω1)| of the entire multistage amplifier circuit at the normalized angular frequency Ω1 2 is expressed by the following Equation (16).

[0053]

Equation

[0054] In Equation (16), Π is a symbol representing the product. Approximating the first-order term of δΩ k in Π(1 + A1δΩ k ) gives the following Equation (17).

[0055]

Equation

[0056] δΩ kSince the average of is zero, the magnitude of the normalized transfer function of the multi-stage amplifier circuit 1 at the normalized angular frequency Ω1 is 1. Therefore, even when the normalized transfer function 0 dB frequencies of the amplifier circuits 2 in each stage are different, but the average of the normalized transfer function 0 dB frequencies of the amplifier circuits 2 in each stage is F1, it is possible to suppress the reduction of the bandwidth and increase the gain as compared with the case of a single-stage amplifier circuit.

[0057] Furthermore, even when the values of the resonance sharpness are different in the amplifier circuits 2 in each stage, if the average of the resonance sharpness of the amplifier circuits 2 in each stage is Q, the magnitude of the normalized transfer function of the multi-stage amplifier circuit 1 at the normalized angular frequency Ω1 becomes 1 by the same approximation as described above, and it is possible to suppress the reduction of the bandwidth and increase the gain as compared with the case of a single-stage amplifier circuit.

[0058] [Second Embodiment] Next, a second embodiment of this embodiment will be described. FIG. 8 is a block diagram showing the configuration of a multi-stage amplifier circuit according to the second embodiment of the present invention. The multi-stage amplifier circuit 1a of this embodiment is formed by connecting a plurality of amplifier circuits 2a having a 0 dB frequency at which the magnitude of the transfer function normalized by the low-frequency gain is 1 at frequencies other than direct current in series between the input terminal 3 and the output terminal 4.

[0059] Each amplifier circuit 2a has a configuration in which two amplifier circuits for generating resonance, an inductance for generating resonance, a capacitive input load, and a resistor for suppressing resonance are connected in series. The circuit model of the amplifier circuit 2a is shown in FIG. 9. The amplifier circuit 2a is composed of a first-stage amplifier circuit 20 and a second-stage amplifier circuit 21 connected to the subsequent stage of the amplifier circuit 20.

[0060] The first-stage amplifier circuit 20 is composed of a main circuit 202 and a resonance inductor L connected between the main circuit 202 and the second-stage amplifier circuit 21. When the main circuit 202 is modeled, as shown in FIG. 9, an input capacitance C connected between the signal input terminal 5 and the ground i and an amplifier section 203 with a gain G that amplifies the signal input to the signal input terminal 5, and an output resistor R with one end connected to the output terminal of the amplifier section 203o and an output resistor R o and an output capacitor C connected between the other end of the output resistor R and ground o are provided to form a configuration.

[0061] Examples of the main circuit 202 include a CMOS inverter amplifier circuit, a FET source-grounded circuit, a differential amplifier circuit, etc. Also, at high frequencies, an emitter-grounded circuit can also be used as the main circuit 202. The main circuit 202 has a constant low-frequency gain G from near DC to the cutoff frequency on the high-frequency side.

[0062] When modeling the second-stage amplifier circuit 21, an input capacitor C connected between the other end of the inductor L and ground is and an amplifier unit 204 with a gain G s (1 + jωL s / R os ) that amplifies the signal input from the amplifier circuit 20, an output resistor R with one end connected to the output terminal of the amplifier unit 204 os and an inductor L with one end connected to the other end of the output resistor R os and the other end connected to the signal output terminal 6, and an output capacitor C connected between the signal output terminal 6 and ground s are provided to form a configuration. A load capacitor C os (the input capacitor C of the next-stage amplifier circuit 2a nx ) is connected to the output of the amplifier circuit 2a. Also, the load capacitor C i of the amplifier circuit 20 nx is the input capacitor C is of the amplifier circuit 21.

[0063] Examples of the amplifier circuit 21 include a CMOS inverter amplifier circuit having a load resistor R os and an inductor L os connected in series to the load resistor R s . Also, a FET source-grounded circuit having an inductor L os connected in series to the load resistor R s , and a FET source-grounded circuit having an inductor L os connected in series to the load resistor R sThe differential amplifier circuit connected can also be used as the amplifier circuit 21. The amplifier circuit 21 has a constant low-frequency gain G from near DC to the cut-off frequency on the high-frequency side. s It has.

[0064] In the amplifier circuit 20, the normalized angular frequency Ω = ω(LC is ) 1 / 2 , the resonance sharpness Q = (L / C is ) 1 / 2 / R o , the output capacitance C o and the input capacitance C of the next stage nx and the ratio k c = C o / C is Then, the square |h(Ω)| of the normalized transfer function of the amplifier circuit 20 2 is represented by Equation (4). The transfer function of the amplifier circuit 21 is represented by the following Equation (18).

[0065]

Equation

[0066] By normalizing Equation (18) with the gain Gs, the normalized transfer function h2(ω) of the amplifier circuit 21 is obtained.

[0067]

Equation

[0068] In the amplifier circuit 21, the normalized angular frequency Ω = ω(LC is ) 1 / 2 = ω{L s (C os + C nx ) / γ} 1 / 2 , the resonance sharpness Q2 = {L s / (C os + C nx )} 1 / 2 / R os , γ = L s (C os + C nx ) / (LC is) Then, the square of the normalized transfer function of the amplifier circuit 21, |h2(Ω)| 2 is represented by the following equation (20).

[0069]

Equation

[0070] Among the normalized transfer function 0 dB frequencies other than DC where the magnitude of the normalized transfer function of the amplifier circuit 20 is 1, the lower frequency F1m is represented by the following equation (21) from equation (5).

[0071]

Equation

[0072] The normalized transfer function 0 dB frequency F2 at which the magnitude of the normalized transfer function of the amplifier circuit 21 becomes 1 is obtained by solving |h2(Ω)| 2 = 1 from equation (20), and is represented by the following equation (22).

[0073]

Equation

[0074] In the amplifier circuit 2a of this embodiment, in order to make the normalized transfer function 0 dB frequencies F1m and F2 equal, the following equation (23) holds.

[0075]

Equation

[0076] By performing a Taylor expansion of the right side of equation (23) with Q = 1, it can be simplified to obtain the following equation (24).

[0077]

Equation

[0078] Also, in this embodiment, the product of the extreme value of the magnitude |h(Ω)| of the normalized transfer function of the amplifier circuit 20 and the extreme value of the magnitude |h2(Ω)| of the normalized transfer function of the amplifier circuit 21 is set to 1 below the frequency F1m. The frequency at which the magnitude |h(Ω)| of the normalized transfer function of the amplifier circuit 20 becomes an extreme value below the frequency F1m is the frequency obtained by dividing Ωa2 in Equation (7) by 2π. The magnitude of the normalized transfer function at this frequency is |h(Ωa2)|.

[0079] The frequency Ωb at which the magnitude |h2(Ω)| of the normalized transfer function of the amplifier circuit 21 becomes an extreme value is obtained by differentiating Equation (20) and is represented by the following Equation (25). The magnitude of the normalized transfer function at this frequency is |h2(Ωb)|. The conditional equation for setting the product of the extreme value of |h(Ω)| and the extreme value of |h2(Ω)| to 1 below the frequency F1m is Equation (26).

[0080]

Equation

[0081]

Equation

[0082] For example, when Q = 1 and k c = 1, 2πF1m = 1, and |h(Ωa2)| -2 = (2 + 3×3 0.5 ) / (3×3 0.5 ). Substituting the values of these Q, kc, and |h(Ωa2)| -2 into Equations (25) and (26) and obtaining Q2 and γ by numerical analysis, we get Q2 = 0.832 and γ = 1.247.

[0083] Q = 1, k cWhen = 1, the normalized transfer function of the amplifier circuit 20 is shown by the broken line 100 in Fig. 10, and the normalized transfer function of the amplifier circuit 21 is shown by the broken line 101 in Fig. 10. The normalized transfer function of the amplifier circuit 20 and the normalized transfer function of the amplifier circuit 21 intersect at the normalized angular frequency Ω = 1 where 2πF1m = 1. It can be seen that below the normalized angular frequency Ω = 1, the normalized transfer function of the amplifier circuit 20 and the normalized transfer function of the amplifier circuit 21 are symmetric with respect to the magnitude 1.

[0084] The transfer function obtained by synthesizing the normalized transfer function of the amplifier circuit 20 and the normalized transfer function of the amplifier circuit 21, that is, the normalized transfer function of the amplifier circuit 2a, is shown by the solid line 102 in Fig. 10. It can be seen that by synthesizing the normalized transfer functions, a normalized transfer function with a small ripple is obtained.

[0085] The normalized transfer function of the amplifier circuit 2a is shown by the broken line 110 in Fig. 11, the normalized transfer function of the multi-stage amplifier circuit 1a with two stages of the amplifier circuit 2a connected is shown by the solid line 111 in Fig. 11, and the normalized transfer function of the multi-stage amplifier circuit 1a with three stages of the amplifier circuit 2a connected is shown by the solid line 112 in Fig. 11.

[0086] According to Fig. 11, it can be seen that even when the number of stages of the amplifier circuit 2a increases, the frequency at which the normalized transfer function becomes 1 does not decrease, and the decrease in the bandwidth due to the multi-stage connection of the amplifier circuit 2a can be suppressed. In the multi-stage amplifier circuit 1a of this embodiment, if the amplification factor of each stage of the amplifier circuit 2a is 1 or more, the decrease in the bandwidth can be suppressed compared with the case of a single-stage amplifier circuit, and the gain can be increased. In the multi-stage amplifier circuit 1a of this embodiment, the gains of the amplifier circuits 2a of each stage do not have to be the same, and the gain G of the amplifier circuit 20 and the gain G of the amplifier circuit 21 that constitute each stage of the amplifier circuit 2a s do not have to be the same.

[0087] In Fig. 9, only the output capacitance C of the main circuit 202 of the first-stage amplifier circuit 20 o is set to k c = 1, but if it is not possible to set only the inherent C of the main circuit 202 o to k c = 1, as shown in Fig. 12, the output capacitance C oAn additional capacitor C o ’ may be connected in parallel. This additional capacitor C o ’ may be a wiring capacitance.

[0088] Q = 1, k c = 1 as the center, when |h(Ωa2)| -2 is Taylor-expanded, the following equation (27) is obtained.

[0089]

Equation

[0090] The conditions of Q and k for which the ripple of the normalized transfer function of the multistage amplifier circuit 1a with two stages of the amplifier circuit 2a connected is reduced c are obtained by numerical analysis using equations (25), (26), and (27), and the following equation (28) is obtained.

[0091]

Equation

[0092] For example, when Q = 0.9, k c = 1.2, |h(Ωa2)| -2 = 1.66, and the conditions of equation (28) are satisfied. The frequency dependence of the normalized transfer function in this case is shown in Fig. 13. The normalized transfer function of the amplifier circuit 2a when Q = 0.9, k c = 1.2 is shown by the dashed line 130 in Fig. 13, and the normalized transfer function of the multistage amplifier circuit 1a with two stages of the amplifier circuit 2a connected is shown by the solid line 131 in Fig. 13. According to Fig. 13, it can be seen that the ripple of the normalized transfer function of the multistage amplifier circuit 1a is suppressed within 3 dB.

[0093] In Fig. 9, only the output capacitance C o of the main circuit 202 of the first-stage amplifier circuit 20 is set to 0.5 < k c ≤ 1.25. However, if it is not possible to set only the inherent C o of the main circuit 202 to 0.5 < k c ≤ 1.25, the output capacitance C is as shown in Fig. 12o An additional capacitor C o ’ may be connected in parallel. This additional capacitor C o ’ may be a wiring capacitance.

Industrial Applicability

[0094] The present invention can be applied to an amplifier circuit.

Explanation of Signs

[0095] 1, 1a... multi-stage amplifier circuit, 2, 2a, 20, 21... amplifier circuit, 5... signal input terminal, 6... signal output terminal, 200, 202... main circuit, 201, 203, 204... amplifier section, L, L s ... inductor, C i , C is ... input capacitance, C o , C os ... output capacitance, R o , R os ... output resistance, C nx ... load capacitance.

Claims

1. It has a configuration in which a plurality of amplifier circuits, for which there exists a 0 dB frequency at which the magnitude of the normalized transfer function normalized by a low-frequency gain becomes 1 at frequencies other than direct current, are connected in series, For each stage of amplifier circuit, when its configuration is represented by a circuit model, an input capacitance connected between a signal input terminal and ground, an amplification unit configured to amplify a signal input to the signal input terminal, an output resistance having one end connected to the output terminal of the amplification unit, an output capacitance connected between the other end of the output resistance and ground, and an inductor having one end connected to the other end of the output resistance and the other end connected to a signal output terminal. A multi-stage amplifier circuit characterized by comprising these components.

2. In the multi-stage amplifier circuit according to Claim 1, let the output resistance be R ｏ , the output capacitance be C ｏ , the inductor be L, and the input capacitance of the next-stage circuit connected to each stage of amplifier circuit be C ｎｘ . When Q = (L / C ｎｘ ) １／２ / R ｏ , and k ｃ = C ｏ / C ｎｘ , the ranges of Q and k ｃ are 【Equation 1】 represented by the following. A multi-stage amplifier circuit characterized by this.

3. In the multi-stage amplifier circuit according to Claim 2, when the 0 dB frequencies of each stage of amplifier circuit are different, and the average of the 0 dB frequencies of each stage of amplifier circuit is F1. A multi-stage amplifier circuit characterized by this.

4. In the multi-stage amplifier circuit according to Claim 2, when the resonance sharpness of each stage of amplifier circuit is different, and the average of the resonance sharpness of each stage of amplifier circuit is the above Q. A multi-stage amplifier circuit characterized by this.

5. A configuration comprising a plurality of amplifier circuits connected in series, where there is a 0 dB frequency at which the magnitude of the normalized transfer function normalized by low-frequency gain becomes 1 at frequencies other than DC. Each stage of the amplifier circuit, when its configuration is represented by a circuit model, includes a first amplifier circuit and a second amplifier circuit connected to the subsequent stage of the first amplifier circuit. The first amplifier circuit includes a first input capacitor connected between the signal input terminal and ground, a first amplification unit configured to amplify the signal input to the signal input terminal, a first output resistor having one end connected to the output terminal of the first amplification unit, a first output capacitor connected between the other end of the first output resistor and ground, and a first inductor having one end connected to the other end of the first output resistor. The second amplifier circuit includes a second input capacitor connected between the other end of the first inductor and ground, a second amplification unit configured to amplify the signal input from the first amplifier circuit, a second output resistor having one end connected to the output terminal of the second amplification unit, a second inductor having one end connected to the other end of the second output resistor and the other end connected to the signal output terminal, and a second output capacitor connected between the signal output terminal and ground. A multi-stage amplifier circuit characterized by this.

6. In the multi-stage amplifier circuit according to Claim 5, the lower of the 0 dB frequencies of the first amplifier circuit is equal to the 0 dB frequency of the second amplifier circuit, and the product of the extreme value of the magnitude of the normalized transfer function of the first amplifier circuit and the extreme value of the magnitude of the normalized transfer function of the second amplifier circuit at the lower frequency is 1. A multi-stage amplifier circuit characterized by this.

7. In the multi-stage amplifier circuit according to Claim 5 or 6, the first output resistor is R ｏ Let the first output capacitance be C ｏ Let the first inductor be L and the second input capacitance be C ｎｘ Let the extreme value of the normalized transfer function of the first amplifier circuit at the lower frequency of the 0 dB frequencies of the first amplifier circuit be |h(Ωa2)|, and Q = (L / C ｎｘ ) １／２ / R ｏ Let k ｃ = C ｏ / C ｎｘ When defined as such, the ranges of Q and k ｃ are [Equation 2] A multi-stage amplifier circuit characterized by being represented by

Images