Multistage amplifier

Abstract

A multistage amplifier (10) according to the present invention comprises, in order, a first amplification unit (11) having a first amplification circuit (111), and a second amplification unit (12) having a second amplification circuit (121). At a frequency that gives an extreme value of a normalized transfer function of the first amplification unit, a normalized transfer function of the second amplification unit has an opposite extreme value. The first amplification unit includes a first amplification circuit, a first inductor connected in parallel to the first amplification circuit, a first resistor, and a second inductor connected in series to the first resistor. The second amplification unit includes a second amplification circuit, a third inductor connected in parallel to the second amplification circuit, and a second resistor.　As a result, the present invention can provide a multistage amplifier capable of suppressing deterioration in frequency characteristics.

Description

Multistage amplifier

[0001] The present invention relates to a multi-stage amplifier for amplifying a baseband signal.

[0002] In communication technologies using electrical signals or optical signals, codes such as NRZ and PAM4, which are baseband signals, are used (for example, Non-Patent Document 1). These codes make it possible to realize a transceiver circuit that can transmit and receive signals with a simple configuration and low latency.

[0003] In the above communication technologies, signal processing such as signal amplification is performed on the receiving side for electrical and optical signals. When there is significant signal attenuation along the communication path, the signal amplitude decreases, so it is necessary to increase the signal amplification gain. Therefore, a configuration in which multiple amplifier circuits for baseband signals are connected in series, i.e., a multi-stage amplifier circuit configuration, is used.

[0004] https: / / ednjapan.com / edn / articles / 1805 / 11 / news018_4.htmlReza Samadi et.al., “Uniform Design of Multi-Peak Bandwidth Enhancement Technique for Multistage Amplifier,” IEEE Transaction on Circuits and Systems Vol. 54, No.7, pp.1489-pp.1499, 2007.

[0005] However, in a configuration in which amplifier circuits are connected in multiple stages (N stages), the bandwidth f_N is f_N=f-3dB(2 １／Ｎ -1) ０．５ Furthermore, in order to achieve high gain and low power consumption, it is necessary to increase the load resistance of the amplifier circuit, but this causes a problem of narrowing the bandwidth.

[0006] In order to solve the above-described problems, a multistage amplifier according to the present invention comprises, in order, a first amplifier unit having a first amplifier circuit and a second amplifier unit having a second amplifier circuit, and at a frequency giving an extreme value of a normalized transfer function of the first amplifier unit, the normalized transfer function of the second amplifier unit has an extreme value opposite to the extreme value.

[0007] Furthermore, a multistage amplifier according to the present invention comprises, in order, a first amplifier unit having a first amplifier circuit and a second amplifier unit having a second amplifier circuit, the first amplifier unit comprising a first amplifier circuit, a first inductor connected in parallel to the first amplifier circuit, a first resistor, and a second inductor connected in series to the first resistor, the first inductor being connected in series with the second amplifier unit, and the second inductor being connected in series to a first DC voltage terminal, the second amplifier unit comprising a second amplifier circuit, a third inductor connected in parallel to the second amplifier circuit, and a second resistor, the third inductor being connected in series with an output terminal, and the second resistor being connected in series to a second DC voltage terminal.

[0008] According to the present invention, it is possible to provide a multistage amplifier that can suppress deterioration of frequency characteristics.

[0009] FIG. 1 is a block diagram showing the configuration of a multistage amplifier according to a first embodiment of the present invention. FIG. 2A is a circuit diagram showing the configuration of a conventional amplifier circuit. FIG. 2B is a circuit diagram showing the configuration of a conventional amplifier circuit. FIG. 3A is a circuit diagram showing the configuration of a conventional amplifier circuit. FIG. 3B is a diagram showing a circuit model of a conventional amplifier circuit. FIG. 4 is a circuit diagram showing the configuration of a conventional amplifier circuit. FIG. 5 is a diagram showing a circuit model of a multistage amplifier according to a first embodiment of the present invention. FIG. 6 is a diagram for explaining the effects of the multistage amplifier according to the first embodiment of the present invention. FIG. 7 is a diagram for explaining the effects of the multistage amplifier according to the first embodiment of the present invention. FIG. 8A is a diagram for explaining the effects of the multistage amplifier according to the first embodiment of the present invention. FIG. 8B is a diagram for explaining the effects of the multistage amplifier according to the first embodiment of the present invention. FIG. 8C is a diagram for explaining the effects of the multistage amplifier according to the first embodiment of the present invention. FIG. 8D is a diagram for explaining the effects of the multistage amplifier according to the first embodiment of the present invention. FIG. 9 is a block diagram showing the configuration of a multistage amplifier according to a second embodiment of the present invention. FIG. 10 is a diagram for explaining the effects of the multistage amplifier according to the second embodiment of the present invention. FIG. 11 is a diagram for explaining the effects of the multistage amplifier according to the second embodiment of the present invention. FIG. 12A is a diagram for explaining the effects of the multistage amplifier according to the second embodiment of the present invention. FIG. 12B is a diagram for explaining the effects of the multistage amplifier according to the second embodiment of the present invention. FIG. 12C is a diagram for explaining the effects of the multistage amplifier according to the second embodiment of the present invention. FIG. 12D is a diagram for explaining the effects of the multistage amplifier according to the second embodiment of the present invention. FIG. 13 is a block diagram showing the configuration of a multistage amplifier according to a third embodiment of the present invention. FIG. 14 is a diagram showing a circuit model of the multistage amplifier according to the third embodiment of the present invention. FIG. 15 is a diagram for explaining the effects of the multistage amplifier according to the third embodiment of the present invention. FIG. 16 is a diagram for explaining the effects of the multistage amplifier according to the third embodiment of the present invention. FIG. 17A is a diagram for explaining the effects of the multistage amplifier according to the third embodiment of the present invention. FIG. 17B is a diagram for explaining the effects of the multistage amplifier according to the third embodiment of the present invention.17C and 17D are diagrams for explaining the effects of the multistage amplifier according to the third embodiment of the present invention.

[0010] First Embodiment A multistage amplifier according to a first embodiment of the present invention will be described with reference to FIGS. 1 to 8D.

[0011] <Configuration of Multistage Amplifier> As shown in FIG. 1, a multistage amplifier 10 according to this embodiment includes a first amplifier section 11 and a second amplifier section 12 connected to the next stage of the first amplifier section 11.

[0012] The first amplifier 11 includes a first amplifier circuit 111, an inductor Lg connected in parallel to the first amplifier circuit 111, and a resistor Rs, and also includes an inductor Ls connected in series to the resistor Rs. The inductor Lg is connected in series to the second amplifier 12 arranged in the next stage. The inductor Ls is connected in series to a DC voltage terminal Vdc1.

[0013] The second amplifier 12 includes a second amplifier circuit 121, an inductor Lg2 connected in parallel to the second amplifier circuit 121, and a resistor Rs2. The inductor Lg2 is connected in series to the output terminal Vo. The resistor Rs2 is connected in series to the DC voltage terminal Vdc2.

[0014] An inverter circuit or a common-source circuit may be used for the first amplifier circuit 111. Similarly, an inverter circuit or a common-source circuit may be used for the second amplifier circuit 121.

[0015] <Effects> The effects of the multistage amplifier 10 according to this embodiment will be described with reference to FIGS. 2 to 8D.

[0016] First, the bandwidth of a conventional amplifier circuit will be described. As an example of a typical transistor circuit used in an amplifier circuit, there is an inverter circuit composed of NMOS and PMOS transistors, as shown in Figure 2A. By biasing the input voltage with an appropriate DC voltage, the input signal Vi is amplified and output.

[0017] Another example of a conventional transistor circuit is a common-source circuit using NMOS transistors, as shown in Figure 2B. This circuit also amplifies and outputs the input signal Vi by biasing the input voltage with an appropriate DC voltage. A common-emitter circuit in which the NMOS transistor is replaced with an npn bipolar transistor may also be used.

[0018] The following describes the bandwidth using an amplifier circuit that also uses an inverter circuit as an example. In an inverter amplifier circuit, as shown in Figure 3A, a resistor Rs is connected between the output Vo and the DC voltage Vdc to adjust the bandwidth and gain. CL is the load capacitance, and when multiple amplifier circuits are connected, it is the sum of the input capacitance of the next amplifier circuit and the capacitance of the connecting wiring. Typically, the DC voltage Vdc is set to be equal to the DC voltage of the output voltage when the input voltage is biased with a DC voltage.

[0019] Figure 3B shows a circuit model of the inverter amplifier circuit in small signal operation. To simplify the analysis, the gate-drain capacitance is ignored. Cd is the sum of the source-drain capacitances of the PMOS and NMOS transistors, and Rd is the resistance between the source and drain of the PMOS and NMOS transistors at the bias point, expressed as a parallel resistance. Equation (1) is obtained from the nodal equation at the output Vo.

[0020]

[0021] where j=(-1) 0.5 From equation (1), equation (2) is obtained.

[0022]

[0023] Here, 1 / Rd+1 / Rs=1 / Rpr, and the gain is gmRpr.

[0024] The angular frequency of the 3 dB band is ω ｃ , frequency f ｃ Then, from the relationship ω=2πf, equation (3) is obtained.

[0025]

[0026] As a result, the gain is proportional to Rpr, while the bandwidth is inversely proportional to Rpr. Therefore, in a conventional inverter amplifier circuit, increasing the gain reduces the bandwidth. Similarly, in the amplifier circuit with a common-source circuit shown in Figure 4, increasing the gain also reduces the bandwidth. Thus, in conventional amplifier circuits, it is difficult to increase the bandwidth along with the gain.

[0027] Next, a description will be given of the multistage amplifier 10 according to this embodiment. Fig. 5 shows a small signal circuit model of the first amplifier section 11. Equation (4) is obtained from the nodal equation at Vo.

[0028]

[0029] From equation (4), equation (5) is obtained.

[0030]

[0031] From the nodal equation at the node of voltage V1, equation (6) is obtained.

[0032]

[0033] From equation (6), equation (7) is obtained.

[0034]

[0035] In equation (7), Rpr=RsRd / (Rs+Rd), and equation (9) is obtained from the relationship expressed by equation (8).

[0036]

[0037]

[0038] In equation (9), when the transfer function (Vo / Vi) is normalized by the gain −gmRpr, the normalized transfer function fo(Ω) is obtained by equation (10).

[0039]

[0040] From equation (4), the transfer function of the second amplifier unit 12 is expressed by equation (11) with Ls=0, Rs=Rs2, Lg=Lg2, gm=gm2, Rd=Rd2, Cd=Cd2, and CL=CL2.

[0041]

[0042] From equation (11), equation (12) is obtained as 1 / Rd2+1 / Rs2=1 / Rpr2.

[0043]

[0044] In equation (12), equation (14) is obtained by normalizing the gain −gmRpr with the relationship expressed by equation (13).

[0045]

[0046]

[0047] Equation (10) and equation (14) are normalized at different resonant frequencies. １ and ω ０ The relationship is expressed by equation (15) using coefficient wg.

[0048]

[0049] In equation (10), ω ０ The relationship with the 3 dB bandwidth of one amplifier stage, which is determined by the CR time constant, is expressed by equation (16) from equation (3).

[0050]

[0051] From equation (16), equation (17) is obtained.

[0052]

[0053] The normalized transfer function of the multistage amplifier 10 according to this embodiment is expressed by equation (18).

[0054]

[0055] FIG. 6 shows the calculation results of the normalized transfer function described above. The vertical axis shows the amplitude of the transfer function normalized by gain (normalized transfer function). The amplitude |f0| (dotted line) of the normalized transfer function of the first amplifier unit 11, the amplitude |f1| (dashed dotted line) of the normalized transfer function of the second amplifier unit 12, and the amplitude |Fs| (solid line) of the normalized transfer function of the multistage amplifier 10 are shown. |f0| was calculated from equation (10), |f1| was calculated from equation (14), and |Fs| was calculated from equation (18). The horizontal axis shows the normalized frequency Ωc calculated from equation (17). Therefore, Ωc=1 on the horizontal axis corresponds to ω=ω ｃ is equivalent to

[0056] The lowest frequency at which the magnitude of the normalized transfer function is 0.7 indicates the 3 dB bandwidth.

[0057] In the calculation, the respective parameters were set as kl=0.3, kc=0.5, Q1=1, γ=0.8, rd=4, kc2=0.9, Q12=0.9, and wg=1.

[0058] In a configuration using only the first amplifier unit 11, Ωc, which indicates a 3 dB bandwidth at the amplitude |f0| of the normalized transfer function, is higher than 1, allowing for a wider bandwidth, but the frequency characteristics are not flat and have large ripples. Similarly, in a configuration using only the second amplifier unit 12, the frequency characteristics are not flat and have large ripples, allowing for a wider bandwidth at |f1|. Furthermore, when a multi-stage amplifier is configured using only the first amplifier unit 11 or only the second amplifier unit 12, the more stages there are, the more the bandwidth deteriorates.

[0059] On the other hand, the normalized transfer function |Fs| of the multistage amplifier 10 is higher than Ωc1, which indicates a 3 dB band, and the ripple in the frequency characteristic is reduced.

[0060] Furthermore, in |Fs|, there exists a frequency (hereinafter referred to as "normalized transfer function 0 dB cross frequency") at which the amplitude of the normalized transfer function becomes 1 other than when the frequency is zero (Ωc=0).

[0061] When amplifiers having a normalized transfer function 0 dB cross frequency are configured in multiple stages, the frequency at which the gain is 1 does not change even if the number of stages increases, and the normalized transfer function 0 dB cross frequency is constant and fixed regardless of the number of stages.

[0062] Ωc, which indicates the 3 dB band when the gain is 0.7, is higher than the normalized transfer function 0 dB cross frequency.

[0063] Therefore, even when the multistage amplifier 10 is configured in multiple stages, the 0 dB cross frequency of the normalized transfer function is constant, and therefore Ωc, which indicates the 3 dB bandwidth in the multistage configuration, remains higher than the 0 dB cross frequency of the normalized transfer function. Thus, even when the multistage amplifier 10 having the 0 dB cross frequency of the normalized transfer function is configured in multiple stages, degradation of the bandwidth is suppressed.

[0064] 7 shows the calculation results of the frequency characteristics of the normalized transfer function of a multistage amplifier configured with multiple stages of the multistage amplifier 10. Calculations were performed on a multistage amplifier configured with two stages, four stages, and six stages, with the multistage amplifier 10 being the multistage amplifier. In the figure, the calculation results for the two-stage, four-stage, and six-stage multistage amplifiers are shown by the solid line, dotted line, and dashed dotted line, respectively.

[0065] In a multistage amplifier consisting of two, four, or six stages, the normalized transfer function 0 dB cross frequency is ω ｃ This is about 1.6 times higher than the previous figure, which is quite high.

[0066] In conventional amplifiers, the ratio of the 3 dB bandwidth of a two-stage amplifier to that of a six-stage amplifier is 0.35 / 0.644≈0.54, and the 3 dB bandwidth of the six-stage amplifier is about half that of the two-stage amplifier.

[0067] On the other hand, in this embodiment, the ratio of the 3 dB bands of the two-stage multistage amplifier and the six-stage multistage amplifier is 1.38 / 1.46≈0.95, and the deterioration of the 3 dB band is suppressed.

[0068] As described above, in this embodiment, when the multistage amplifier 10 including the first amplifying section 11 and the second amplifying section 12 is configured in multiple stages, deterioration of the band is suppressed.

[0069] The multistage amplifier according to this embodiment can achieve a wider bandwidth than a single amplifier, and even if a multistage configuration is used to achieve a high gain, degradation of the bandwidth can be suppressed.

[0070] Next, the frequency characteristics of the normalized transfer function when the parameters are changed in the case where the multistage amplifier 10 according to this embodiment is configured in multiple stages will be described.

[0071] Figures 8A to 8D show the calculation results of the frequency characteristics of the normalized transfer function when the parameters are changed. In the calculation of Figure 7, rd was changed from 2 to 50 (Figure 8A), kl from 0.1 to 1 (Figure 8B), kc from 0.1 to 1.6 (Figure 8C), and Q1 from 0.7 to 1.5 (Figure 8D).

[0072] 8A to 8D, 0.9≦|Fs|≦1.1 is satisfied for any change in the parameters. Even when a six-stage multistage amplifier is constructed using three two-stage amplifiers having these parameters, |Fs| ３ The ripple is 0.9 ３ = 0.729 to 1.1 ３ = 1.33, which is within ±3 dB.

[0073] Thus, according to the multistage amplifier of this embodiment, even when the multistage amplifier is configured in multiple stages, the 3 dB band is higher than the 0 dB cross frequency of the normalized transfer function, and degradation of the band is also suppressed.

[0074] The conditions for reducing ripples are explained below. If the normalized frequencies that give extreme values ​​of |f0| and |f1| are similar, and |f0|·|f1| is close to 1 at the normalized frequency Ωp that gives the extreme value of |f0|, the ripple of |Fs| is small. Therefore, it is sufficient that |f0| is at its maximum value when |f1| is at its minimum value, and that |f0| is at its minimum value when |f1| is at its maximum value. In this way, it is sufficient that the extreme values ​​of |f1| and |f0| take opposite extreme values.

[0075] As shown in Figure 6, |f1| is a minimum value at the minimum frequency that gives an extreme value to |f1| other than DC (when the frequency is zero). In order to reduce ripple, |f0| needs to be a maximum value at the minimum frequency that gives an extreme value. To achieve this, it is sufficient that Ω << 1 and |f0| > 1. |f0| ２ The condition for |f0|>1 is expressed by equation (19) by approximating up to the second-order term of Ω using the numerator and denominator of

[0076]

[0077] From equation (19), equations (20) and (21) are obtained.

[0078]

[0079]

[0080] Next, find the frequency that gives the extreme value of |f0|. From equation (10), the real term Hre and the imaginary term Him are expressed as Ω ２ Approximating up to the term, it is expressed by equation (22).

[0081]

[0082] From the solution where the differential of equation (22) becomes zero, the frequency Ωp that gives the peak is expressed by equation (23).

[0083]

[0084] From equation (23), equation (24) is obtained.

[0085]

[0086] Next, the frequency at which |f1| has an extreme value is found. ２ is expressed by equation (25).

[0087]

[0088] From the solution where the differential of equation (25) becomes zero, the frequency Ω1 that gives the peak is expressed by equation (26).

[0089]

[0090] From equation (26), equation (27) is obtained.

[0091]

[0092] ω １ The normalized frequency Ω1p that gives an extreme value at the frequency normalized by is expressed by equation (28).

[0093]

[0094] ω １ and ω ０ From the relationship of ω ０ The normalized frequency Ω1p0 that gives an extreme value at the frequency normalized by is expressed by equation (29).

[0095]

[0096] The frequency Ωp giving the extreme value of |f0| in equation (24) and the frequency wg Ω1p giving the extreme value of |f1| in equation (29) are allowed within the range shown in equation (30).

[0097]

[0098] Furthermore, at the frequency Ωp that gives an extreme value at |f0|, if |f0(Ωp)|·|f1(Ωp)| is between 0.9 and 1.1, the ripple is reduced. From equations (22) and (25), equation (3) is obtained.

[0099]

[0100] In the multistage amplifier 10, ripples can be reduced and bandwidth degradation can be suppressed by setting the amplitudes of the normalized transfer function of the first amplifier unit 11 and the normalized transfer function of the second amplifier unit 12 to predetermined values ​​at the frequency at which the normalized transfer function of the first amplifier unit 11 takes an extreme value. It is desirable that the product of the amplitude of the normalized transfer function of the first amplifier unit 11 and the amplitude of the normalized transfer function of the second amplifier unit 12 be a predetermined value.

[0101] Furthermore, in the multistage amplifier 10, at the frequency at which the normalized transfer function of the first amplifier unit 11 has an extreme value, the normalized transfer function of the second amplifier unit 12 has an extreme value opposite to the extreme value, thereby reducing ripples and suppressing bandwidth degradation.

[0102] According to the multistage amplifier of this embodiment, it is possible to suppress deterioration of the band.

[0103] Second Embodiment A multistage amplifier according to a second embodiment of the present invention will be described with reference to FIGS. 9 to 12D.

[0104] <Configuration of Multistage Amplifier> As shown in FIG. 9 , the multistage amplifier 20 according to this embodiment has the same configuration as the multistage amplifier according to the first embodiment, except that an inductor Ls2 is connected between the resistor Rs of the second amplifying section 22 and the DC voltage terminal Vdc2.

[0105] <Effects> In the first embodiment, the normalized transfer function of the second amplifier unit 22 is at a minimum value at the smallest frequency other than DC that gives an extreme value, and therefore, the ripple is reduced by applying a condition under which the normalized transfer function of the first amplifier unit 11 is at a maximum value.

[0106] In this embodiment, at the smallest frequency other than DC that gives an extreme value, if the normalized transfer function of the first amplifier unit 11 is a maximum value, the normalized transfer function of the second amplifier unit 22 must be a minimum value, and if the normalized transfer function of the first amplifier unit 11 is a minimum value, the normalized transfer function of the second amplifier unit 22 must be a maximum value.

[0107] The normalized transfer functions of the first amplifier 11 and the second amplifier 22 have different coefficients in equation (10). The coefficients of the first amplifier 11 are the same as those in equation (8). The coefficients of the second amplifier 22 are as shown in equation (32).

[0108]

[0109] 10 shows the calculation results of the normalized transfer functions of the first amplifier unit 11, the second amplifier unit 22, and the multistage amplifier 20. The vertical axis shows the amplitude |f0| (dotted line) of the normalized transfer function of the first amplifier unit 11, the amplitude |f1| (dashed dotted line) of the normalized transfer function of the second amplifier unit 22, and the amplitude |Fs| (solid line) of the normalized transfer function of the multistage amplifier 20. The horizontal axis shows the normalized frequency Ωc, where Ωc=1 corresponds to ω=ω. ｃ The lowest frequency at which the amplitude of the normalized transfer function is 0.7 indicates the 3 dB bandwidth.

[0110] In a configuration using only the first amplifier unit 11, Ωc, which indicates a 3 dB bandwidth at the amplitude |f0| of the normalized transfer function, is higher than 1, allowing for a wider bandwidth, but the frequency characteristics are not flat and have large ripples. Similarly, in a configuration using only the second amplifier unit 22, the frequency characteristics are not flat and have large ripples, allowing for a wider bandwidth at |f1|. Furthermore, when a multistage amplifier is configured using only the first amplifier unit 11 or only the second amplifier unit 22, the more stages there are, the more the bandwidth deteriorates (Non-Patent Document 2).

[0111] Furthermore, in |Fs|, there exists a frequency (hereinafter referred to as "normalized transfer function 0 dB cross frequency") at which the amplitude of the normalized transfer function becomes 1 other than when the frequency is zero (Ωc=0).

[0112] When amplifiers having a normalized transfer function 0 dB cross frequency are configured in multiple stages, the frequency at which the gain is 1 does not change even if the number of stages increases, and the normalized transfer function 0 dB cross frequency is constant and fixed regardless of the number of stages.

[0113] Ωc, which indicates the 3 dB band when the gain is 0.7, is higher than the normalized transfer function 0 dB cross frequency.

[0114] Therefore, even when the multistage amplifier 20 is configured in multiple stages, the 0 dB cross frequency of the normalized transfer function is constant, and therefore Ωc, which indicates the 3 dB bandwidth in the multistage configuration, remains higher than the 0 dB cross frequency of the normalized transfer function. Thus, even when the multistage amplifier 20 having the 0 dB cross frequency of the normalized transfer function is configured in multiple stages, degradation of the bandwidth is suppressed.

[0115] 11 shows the calculation results of the frequency characteristics of the normalized transfer function of a multistage amplifier configured with multiple stages of multistage amplifier 20. Calculations were performed for multistage amplifiers configured with two stages, four stages, and six stages of multistage amplifier 20. In the figure, the calculation results for the two-stage, four-stage, and six-stage multistage amplifiers are shown by the solid line, dotted line, and dashed dotted line, respectively.

[0116] In a multistage amplifier consisting of two, four, or six stages, the normalized transfer function 0 dB cross frequency is ω ｃ , which is about twice the 0 dB cross frequency (ω ｃ This is about 1.6 times higher than the previous figure.

[0117] As described above, in this embodiment, when the multistage amplifier 20 including the first amplifying section 11 and the second amplifying section 22 is configured in multiple stages, deterioration of the band is suppressed.

[0118] The multistage amplifier according to this embodiment can achieve a wider bandwidth than a single amplifier, and even if a multistage configuration is used to achieve a high gain, degradation of the bandwidth can be suppressed.

[0119] Next, the frequency characteristics of the normalized transfer function when the parameters are changed in the case where the multistage amplifier according to this embodiment is configured in multiple stages will be described.

[0120] Figures 12A to 12D show the calculation results of the frequency characteristics of the normalized transfer function when the parameters are changed. Calculations were performed by changing rd from 2 to 50 (Figure 12A), kl from 0.1 to 1 (Figure 12B), kc from 0.1 to 1.6 (Figure 12C), and Ql from 0.75 to 1.45 (Figure 12D).

[0121] 12A to 12D, 0.9≦|Fs|≦1.1 is satisfied for any change in the parameters. Even when a six-stage multistage amplifier is constructed using three two-stage amplifiers having these parameters, |Fs| ３ The ripple is 0.9 ３ = 0.729 to 1.1 ３ = 1.33, which is within ±3 dB.

[0122] Thus, according to the multistage amplifier of this embodiment, even when the multistage amplifier is configured in multiple stages, the 3 dB band is higher than the 0 dB cross frequency of the normalized transfer function, and degradation of the band is also suppressed.

[0123] Third Embodiment A multistage amplifier according to a third embodiment of the present invention will be described with reference to FIGS. 13 to 17D.

[0124] <Configuration of Multistage Amplifier> As shown in FIG. 13 , in a multistage amplifier 30 according to this embodiment, in the first amplifying section of the multistage amplifier according to the second embodiment, a resistor R1 and an inductor L1 are connected in series between an inductor Lg and the input of a second amplifying section 22 in the next stage, and a capacitor C1 is connected between the node of the inductor Lg and the resistor R1 and ground.

[0125] <Effects> Next, we will explain the normalized transfer function of the first amplifier unit 31. Fig. 14 shows a circuit model of the first amplifier unit 31. From the nodal equation at the output Vo, equation (33) is obtained.

[0126]

[0127] From equation (33), equation (34) is obtained.

[0128]

[0129] From the nodal equation at output V2, equation (35) is obtained.

[0130]

[0131] From equation (35), equation (36) is obtained.

[0132]

[0133] From the nodal equation at output V1, equation (37) is obtained.

[0134]

[0135] On the right side of equation (37), the real part Hre(ω) and the imaginary part Him(ω) are expressed by equations (38) and (39).

[0136]

[0137]

[0138] The relationship between the input signal Vi and the output signal Vo is expressed by equation (40).

[0139]

[0140] By normalizing equation (40) by the gain, the normalized transfer function f0 is obtained as equation (41).

[0141]

[0142] In equation (41), by normalizing each parameter by equation (42), equations (43) to (45) are obtained.

[0143]

[0144]

[0145]

[0146]

[0147] The normalized transfer function of the second amplifier is the same as that in the second embodiment.

[0148] 15 shows the calculation results of the normalized transfer functions of the first amplifier unit 31, the second amplifier unit 22, and the multistage amplifier 30. The vertical axis shows the amplitude |f0| (dotted line) of the normalized transfer function of the first amplifier unit 31, the amplitude |f1| (dashed-dotted line) of the normalized transfer function of the second amplifier unit 22, and the amplitude |Fs| (solid line) of the normalized transfer function of the multistage amplifier 30. The horizontal axis shows the normalized frequency Ωc, where Ωc = 1 corresponds to ω = ωc. The minimum frequency at which the amplitude of the normalized transfer function is 0.7 indicates the 3 dB bandwidth.

[0149] In the calculation, the respective parameters were set as klg = 0.5, kl1 = 0.7, kc1 = 0.6, kcd = 1.3, Q1 = 0.86, γ = 0.75, rd = 4, r1 = 0.2, ks = 0.35, kc2 = 0.9, Q12 = 0.75, rd = 4, and wg = 0.8.

[0150] In a configuration using only the first amplifier unit 31, Ωc, which indicates a 3 dB bandwidth at the amplitude |f0| of the normalized transfer function, is higher than 1, allowing for a wider bandwidth, but the frequency characteristics are not flat and have large ripples. Similarly, in a configuration using only the second amplifier unit 22, the frequency characteristics are not flat and have large ripples, allowing for a wider bandwidth at |f1|. Furthermore, when a multistage amplifier is configured using only the first amplifier unit 31 or only the second amplifier unit 22, the more stages there are, the more the bandwidth deteriorates (Non-Patent Document 2).

[0151] On the other hand, the normalized transfer function |Fs| of the multistage amplifier 30 is higher than Ωc1, which indicates a 3 dB band, and the ripple in the frequency characteristic is reduced.

[0152] Furthermore, in |Fs|, there exists a frequency (normalized transfer function 0 dB cross frequency) at which the amplitude of the normalized transfer function becomes 1 when the frequency is other than zero (Ωc=0).

[0153] When amplifiers having a normalized transfer function 0 dB cross frequency are configured in multiple stages, the frequency at which the gain is 1 does not change even if the number of stages increases, and the normalized transfer function 0 dB cross frequency is constant and fixed regardless of the number of stages.

[0154] Ωc, which indicates the 3 dB band when the gain is 0.7, is higher than the normalized transfer function 0 dB cross frequency.

[0155] Therefore, even when the multistage amplifier 30 is configured in multiple stages, the 0 dB cross frequency of the normalized transfer function is constant, and therefore Ωc, which indicates the 3 dB bandwidth in the multistage configuration, remains higher than the 0 dB cross frequency of the normalized transfer function. Thus, even when the multistage amplifier 30 having the 0 dB cross frequency of the normalized transfer function is configured in multiple stages, degradation of the bandwidth is suppressed.

[0156] 16 shows the calculation results of the frequency characteristics of the normalized transfer function of a multistage amplifier configured with multiple stages of the multistage amplifier 30. Calculations were performed for multistage amplifiers configured with two stages, four stages, and six stages of the multistage amplifier 30. In the figure, the calculation results for the two-stage, four-stage, and six-stage multistage amplifiers are shown by the solid line, dotted line, and dashed dotted line, respectively.

[0157] In a multistage amplifier consisting of two, four, or six stages, the normalized transfer function 0 dB cross frequency is ω ｃ This is about 2.2 times higher than the first embodiment (about 1.6) and the second embodiment (about 2.0).

[0158] On the other hand, in this embodiment, the ratio of the 3 dB bandwidth of the two-stage multistage amplifier to the six-stage multistage amplifier is 2.38 / 2.57 ≈ 0.93, which suppresses the deterioration of the 3 dB bandwidth compared to the conventional amplifier (0.54).

[0159] In this manner, in this embodiment, when the multistage amplifier 30 including the first amplifying section 31 and the second amplifying section 22 is configured in multiple stages, deterioration of the band is suppressed.

[0160] The multistage amplifier according to this embodiment can achieve a wider bandwidth than a single amplifier, and even if a multistage configuration is used to achieve a high gain, degradation of the bandwidth can be suppressed.

[0161] Next, the frequency characteristics of the normalized transfer function when the parameters are changed in the case where the multistage amplifier according to this embodiment is configured in multiple stages will be described.

[0162] 17A to 17D show the calculation results of the frequency characteristics of the normalized transfer function when the parameters are changed. Calculations were performed by changing rd from 2 to 50 (FIG. 17A), kl from 0.1 to 1 (FIG. 17B), kc from 0.1 to 1.6 (FIG. 17C), and Ql from 0.75 to 1.45 (FIG. 17D).

[0163] 17A to 17D, 0.9≦|Fs|≦1.1 is satisfied for any change in the parameters. Even when a six-stage multistage amplifier is constructed using three two-stage amplifiers having these parameters, |Fs| ３ The ripple is 0.9 ３ = 0.729 to 1.1 ３ = 1.33, which is within ±3 dB.

[0164] Thus, according to the multistage amplifier of this embodiment, even when the multistage amplifier is configured in multiple stages, the 3 dB band is higher than the 0 dB cross frequency of the normalized transfer function, and degradation of the band is also suppressed.

[0165] In this embodiment, an example in which the second amplifier unit of the second embodiment is used has been shown, but the present invention is not limited to this, and the second amplifier unit of the first embodiment may also be used.

[0166] In the multistage amplifier according to the embodiment of the present invention, at a frequency that gives an extreme value of the normalized transfer function of the first amplifier unit, the normalized transfer function of the second amplifier unit has an extreme value that is opposite to the extreme value, thereby reducing ripples and suppressing bandwidth degradation.

[0167] In the embodiments of the present invention, examples of the structure, dimensions, materials, etc. of each component in the configuration of the multistage amplifier etc. have been shown, but the present invention is not limited to these examples. Anything that can demonstrate the function and effect of the multistage amplifier may be used.

[0168] It should be noted that the present invention is not limited to the above-described embodiments, and it is apparent that many modifications and combinations can be made by those skilled in the art within the technical scope of the present invention. For example, the third embodiment may be combined with the first embodiment.

[0169] A part or all of the above-described embodiment or an example thereof can be described as, but is not limited to, the following supplementary notes.

[0170] (Supplementary Note 1) A multi-stage amplifier comprising, in order, a first amplifier unit having a first amplifier circuit and a second amplifier unit having a second amplifier circuit, wherein at a frequency giving an extreme value of a normalized transfer function of the first amplifier unit, the normalized transfer function of the second amplifier unit has an extreme value opposite to the extreme value.

[0171] (Supplementary Note 2) A multi-stage amplifier comprising, in order, a first amplifier unit having a first amplifier circuit and a second amplifier unit having a second amplifier circuit, the first amplifier unit comprising a first amplifier circuit, a first inductor connected in parallel to the first amplifier circuit, and a first resistor, and a second inductor connected in series to the first resistor, the first inductor connected in series with the second amplifier unit, and the second inductor connected in series to a first DC voltage terminal, the second amplifier unit comprising a second amplifier circuit, a third inductor connected in parallel to the second amplifier circuit, and a second resistor, the third inductor connected in series with an output terminal, and the second resistor connected in series to a second DC voltage terminal.

[0172] (Supplementary Note 3) The multistage amplifier according to Supplementary Note 2, wherein a fourth inductor is connected between the second resistor and the second DC voltage terminal.

[0173] (Supplementary Note 4) The multi-stage amplifier according to Supplementary Note 2 or Supplementary Note 3, wherein a third resistor and a fifth inductor are connected in series between the first inductor and the second amplifying unit, and a capacitance is connected between a node between the first inductor and the third resistor and ground.

[0174] (Supplementary Note 5) A multistage amplifier comprising, in order, a first amplifier unit having a first amplifier circuit and a second amplifier unit having a second amplifier circuit, wherein, at a frequency giving an extreme value of a normalized transfer function of the first amplifier unit, the amplitude of the normalized transfer function of the first amplifier unit and the amplitude of the normalized transfer function of the second amplifier unit are set to predetermined values ​​so as to suppress deterioration of frequency characteristics.

[0175] (Supplementary Note 6) The multistage amplifier according to Supplementary Note 5, wherein the product of the amplitude of the normalized transfer function of the first amplifier unit and the amplitude of the normalized transfer function of the second amplifier unit is set to a predetermined value.

[0176] (Supplementary Note 7) The multistage amplifier according to Supplementary Note 6, wherein the value of the product is equal to or greater than 0.9 and equal to or less than 1.1.

[0177] The present invention relates to a multistage amplifier for amplifying a baseband signal, and can be applied to a communication device or a communication system.

[0178] 10 Multistage amplifier 11 First amplifier section 111 First amplifier circuit 12 Second amplifier section 121 Second amplifier circuit

Claims

1. A multi-stage amplifier comprising, in order, a first amplifier unit having a first amplifier circuit and a second amplifier unit having a second amplifier circuit, wherein at a frequency giving an extreme value of the normalized transfer function of the first amplifier unit, the normalized transfer function of the second amplifier unit has an extreme value opposite to the extreme value.

2. A multi-stage amplifier comprising, in order, a first amplifier unit having a first amplifier circuit, and a second amplifier unit having a second amplifier circuit, wherein the first amplifier unit comprises a first amplifier circuit, a first inductor connected in parallel to the first amplifier circuit, a first resistor, and a second inductor connected in series to the first resistor, the first inductor being connected in series with the second amplifier unit, and the second inductor being connected in series to a first DC voltage terminal, and the second amplifier unit comprises a second amplifier circuit, a third inductor connected in parallel to the second amplifier circuit, and a second resistor, the third inductor being connected in series with an output terminal, and the second resistor being connected in series to a second DC voltage terminal.

3. The multi-stage amplifier according to claim 2, wherein a fourth inductor is connected between said second resistor and said second DC voltage terminal.

4. A multistage amplifier according to claim 2 or 3, wherein a third resistor and a fifth inductor are connected in series between the first inductor and the second amplifying section, and a capacitance is connected between the node between the first inductor and the third resistor and ground.

Images