Abstract:
In the optical modulator driver, a plurality of differential amplifiers are arranged in one direction, and input terminals and output terminals of each adjacent differential amplifier are connected via independent wirings. Each differential amplifier includes a differential pair and a series circuit. In the series circuit, a resistor, a capacitor, and a resistor are connected in series. The series circuit is provided between emitters of two transistors of the differential pair, one of the differential input terminals of the differential amplifier and one transistor of the differential pair are connected via a resistor, and the other of the differential input terminals of the differential amplifier and the other transistor of the differential pair are connected via a resistor.

Description:
TECHNICAL FIELD 
     The present invention relates to an optical modulator driver that is used for an optical transmitter or the like. 
     BACKGROUND 
     In communication between servers in a data center and optical transmission systems constituting a core network, an optical transceiver to perform mutual conversion between an electric signal and an optical signal and to perform transmission and reception of the optical signal is heavily used in a physical layer of an OSI reference model. The optical transceiver includes a transmission part (optical transmitter) and a reception part (optical receiver). The optical transmitter includes a light source such as a semiconductor laser, an optical modulator to modulate CW (Continuous Wave) light output from the light source in response to a driving voltage and emit modulated CW light (optical signal), and an optical modulator driver to generate the driving voltage according to an electric signal and provide a bias voltage to be a reference voltage thereof. The optical transmitter converts the electric signal into the optical signal and transmit the optical signal to an optical waveguide such as an optical fiber (this corresponds to the case of an external modulation system (refer to  FIG. 1 )). 
     In order to drive the optical modulator at a symbol rate of 25 [Gbaud] or 40 [Gbaud], for example, a superior quality of waveforms such as high-speed falling/rising and low jitter is required in waveforms of driving signals. For this reason, it is necessary to suppress a reflection coefficient of a high frequency signal small up to a frequency of about 40 [GHz] for example. Patent Literature 1-3 disclosed driving techniques to suppress an S parameter S 22  of a driver and an S parameter S 11  of the optical modulator. 
     Patent Literature 1 disclosed technology for applying a technique of a travelling wave amplifier (TWA) to a differential amplifier. The TWA includes transmission lines formed between input terminals of a plurality of transistors and between output terminals thereof to broaden bandwidth. Patent Literature 2 disclosed a method of improving a frequency characteristic in a high frequency region when a TWA of a differential type (semiconductor IC chip) is mounted on a package (not illustrated in the drawings). Patent Literature 3 disclosed a capacitive source degeneration circuit as technology for improving a frequency characteristic having a right-downward slope caused by signal attenuation in an input transmission line (not illustrated in the drawings). 
     Digital coherent optical transmission systems having a large capacity of communication and a high speed performance have been developed for practical use to deal with a rapidly increasing demand of communication traffic for a network. Such digital coherent optical transmission systems have been incorporating PAM-4 (4-level Pulse Amplitude Modulation) and 16-QAM (16-level Quadrature Amplitude Modulation) as a modulation system. 
     Patent Literature 1: Japanese Patent Application Laid-Open No. H09-130170, 
     Patent Literature 2: Japanese Patent No. 4965602, 
     Patent Literature 3: Japanese Patent No. 4952713. 
     SUMMARY 
     As the optical modulator driver using the TWA according to the related art, a structure of a TWA is illustrated in  FIG. 2 . An optical modulator driver illustrated in  FIG. 2  includes differential amplifiers Cell- 1  to Cell- 4  connected in parallel to each other, output transmission lines Lout 0  to Lout 3  and Loutb 0  to Loutb 3 , input transmission lines Lin 1  to Lin 4  and Linb 1  to Linb 4 , terminal resistors Re 1  to Re 4 , a positive-phase input terminal Din, a negative-phase input terminal Dinb, a positive-phase output terminal Dout, and a negative-phase output terminal Doutb. The output transmission lines Lout 0  to Lout 3  and Loutb 0  to Loutb 3  are transmission lines of characteristic impedance 50 ohm each constituting a distributed constant circuit having inductances of individual wirings and output capacitances (about 20 [fF]) of the respective differential amplifiers Cell- 1  to Cell- 4 . The input transmission lines Lin 1  to Lin 4  and Linb 1  to Linb 4  are transmission lines constituting a distributed constant circuit having inductances of individual wirings and input capacitances (about 20 [fF]) of the respective differential amplifiers Cell- 1  to Cell- 4 . The signals each amplified by the respective differential amplifiers Cell- 1  to Cell- 4  have delay times equal to each other. In addition, delay times of the individual transmission lines are designed such that the delay times are equal to each other at the corresponding input sides and output sides. That is, respective delay times of Lout 1  and Loutb 1  and Lin 1  and Linb 1  are equal to each other, respective delay times of Lout 2  and Loutb 2  and Lin 2  and Linb 2  are equal to each other, and respective delay times of Lout 3  and Loutb 3  and Lin 3  and Linb 3  are equal to each other. 
     The respective delay times of the differential amplifier and the transmission lines are adjusted as described above, so that the signals input to the positive-phase input terminal Din and the negative-phase input terminal Dinb reaches the respective differential amplifier (Cell- 1  to Cell- 4 ) at different phases and the amplified signals output from the respective differential amplifier are superimposed at the same phases in the positive-phase output terminal Dout and in the negative-phase output terminal Doutb, respectively. In multi-level modulation such as PAM-4 and 16QAM using the optical modulator driver (travelling wave amplifier) illustrated in  FIG. 2 , a communication signals has logic levels of 2N (N=2, 3, 4, . . . ) provided in a direction of amplitude thereof. An interval between any two logic levels adjacent to each other may be constant to restrain an identification error for each logic level. For this reason, the optical modulator driver needs to execute linear amplification. 
     For example, in  FIG. 3  (the case of PAM-4), a differential input voltage Vin-Vinb (horizontal axis) and a differential output voltage Vout-Voutb (vertical axis) have four logic levels (inputs In 0  to In 3  and outputs Out 0  to Out 3 ), respectively. However, if an right-upward part (a slope Δ(Vout−Voutb)/Δ(Vin−Vinb) corresponds to voltage gain) of a curved line becomes a linear form (straight line) for the entire voltage range of input signals from In 0  to In 3 , the respective logic levels are transferred to output signals at the same ratio, while as deviating from the linear form (straight line), the ratio changes depending on the logic levels and waveforms of the output signals are distorted. To perform such linear amplification, the voltage gain of the differential amplifier is set to be smaller than the voltage gain in the case of a saturated operation (broken line). The above explanation referring  FIG. 3  has been made for static characteristics. However, because actual modulation is performed by a high-speed pulse signal, frequency characteristics of voltage gain should be flat in a predetermined frequency region. That is, the slope (voltage gain) of the right-upward part of  FIG. 3  may be constant for high frequency components of the high-speed pulse signal. Here, Vin shows a positive-phase input voltage input to a positive-phase input terminal Din, Vinb shows a negative-phase input voltage input to a negative-phase input terminal Dinb, and the positive-phase input voltage Vin and the negative-phase input voltage Vinb are complementary voltage signals that have phases opposite to each other. In addition, Vout shows a positive-phase output voltage output from a positive-phase output terminal Dout, Voutb shows a negative-phase output voltage output from a negative-phase output terminal. Doutb, and the positive-phase output voltage Vout and the negative-phase output voltage Voutb are complementary voltage signals that have phases opposite to each other. 
     Meanwhile, the inventors have discovered that, decrease of voltage gain in the linear amplification performed by a differential amplifier degrades a common-mode rejection ratio (CMRR) in a high frequency region of 5 [GHz] or more and jitter of waveforms of output signals increases. The degradation of CMRR causes increase of an identification error of an optical receiver. The CMRR means that a characteristic is good when a value thereof is large.  FIG. 4  illustrates a block diagram of a transmission part including a digital to analog converter (DAC) to generate a differential signal input to the optical modulator driver using the TWA illustrated in  FIG. 2 . A differential signal output from the DAC is a multi-level modulated signal. After passing through a high-frequency transmission line, the differential signal is input to the optical modulator driver. At this time, due to a difference (skew) of delay times of a positive-phase signal (Vout) side and a negative-phase signal (Voutb) side of the high-frequency transmission line and unbalance of a positive-phase signal and a negative-phase signal of DAC output terminals (DAC-Dout and DAC-Doutb), the differential signal input to the optical modulator driver includes common-mode components, in addition to the original components of the differential signal. The CMRR is represented by the following formula (formula 1):
 
CMRR=20×log 10 ( Ad/Ac )  (formula 1),
 
where Ad is differential voltage gain defined as a ratio of a differential component of an output voltage signal to a differential component of an input voltage signal, Ac is common-mode voltage gain defined as a ratio of a common-mode component of the output voltage signal to a common-mode component of the input voltage signal.
 
     In addition, the inventors have discovered that the CMRR mainly depends on a characteristic of a current source of each differential amplifier in the optical modulator driver using the TWA illustrated in  FIG. 2 . An example of a circuit structure of each differential amplifier of the optical modulator driver using the TWA illustrated in  FIG. 2  is illustrated in  FIG. 5  (Because the circuit structure of the differential amplifier illustrated in  FIG. 5  is partially equal to a circuit structure illustrated in  FIG. 8 , the circuit structure will be described in detail below with reference to  FIG. 8 ). Each differential amplifier includes a differential input terminal Da, a differential pair Db, an emitter follower Dc to drive the differential pair Db (emitters of transistors Tr 3  and Tr 4  are connected via resistors R 1  and R 2 ), two cascade transistors (bases of transistors Tr 5  and Tr 6  are connected to each other) each connected to respective collectors of the differential pair Db, a current source Is, and a differential output terminal Dd. The differential input terminal Da includes a positive-phase input terminal Cell-in and a negative-phase input terminal Cell-inb. The differential output terminal Dd includes a positive-phase output terminal Cell-out and a negative-phase output terminal Cell-outb. The current source Is is connected to a connecting point of the resistors R 1 , R 2  of the differential pair Db and provides a current to the differential pair Db. The current source Is with a transistor Tr 7  is considered as an equivalent circuit including parasitic components (a capacitance Cbc and an impedance Zc 2 ) illustrated in  FIG. 6 , due to electrical characteristics of the transistor Tr 7 . The capacitance Cbc is a parasitic capacitance between base and collector of the transistor Tr 7 . The impedance Zc 2  is impedance determined by considering a feedback signal by Gm (voltage-to-current gain (ΔIce/ΔVbe) of the transistor Tr 7 ) of the transistor Tr 7 . At a frequency of about 20 [GHz], the impedance Zc 2  is taken to be low as compared with the capacitance Cbc. It has been discovered that the CMRR depends on characteristics of the current source Is. 
       FIGS. 7A, 7B  illustrate simulation results of frequency characteristics (Ac, Ad, and CMRR) of an optical modulator driver using a TWA for a linear amplification system. In  FIG. 7A , a horizontal axis shows a frequency [GHz] of an input signal and a vertical axis shows voltage gain [dB] of an output signal. In  FIG. 7A , a curve Ac 1  shows a result of common-mode voltage gain Ac for the circuit structure of  FIG. 5 , a curve Ad 1  shows a result of differential voltage gain Ad, and a curve Ach shows a result of common-mode voltage gain Ach in the case of using an ideal current source Is not including the parasitic components (the capacitance Cbc and the impedance Zc 2 ) illustrated in  FIG. 6 , for a comparison. In  FIG. 7B , a horizontal axis shows a frequency [GHz] of an input signal and a vertical axis shows a CMRR. [dB] obtained by the results illustrated in  FIG. 7A . In  FIG. 7B , a curve Cr 1  shows a CMRR calculated from the results of the curves Ac 1 , Ad 1  of  FIG. 7A  using the formula 1 and a curve Crh shows a CMRR calculated from the results of the curves Ach, Ad 1  of  FIG. 7A  using the formula 1. 
     Referring to  FIGS. 7A and 7B , Ac increases by an influence of the capacitance Cbc and the impedance Zc 2  at a high frequency and the CMRR decreases accordingly. For example, when the optical modulator driver using a TWA performs a modulation operation at 32 [Gbaud], a common-mode component by the above-mentioned skew appears in a frequency region of 10 to 30 [GHz]. However, in the frequency region, the CMRR causes a difference of 6 to 13 [dB] according to presence or absence of the parasitic components. 
     Accordingly, the present invention has been made in view of the above problems and an object of the present invention is to provide an optical modulator driver that increases a common-mode rejection ratio in a high frequency region and performs liner amplification suitable for pulse amplitude modulation. 
     An optical modulator driver according to one embodiment of the present invention is an optical modulator driver in which at least two differential amplifiers each of which includes a differential input terminal (a pair of input terminals) and a differential output terminal (a pair of output terminals) are provided, a differential signal input from the outside are input to the respective differential input terminals via input transmission lines, and differential signals output from the output terminals of the respective differential amplifiers are output to the outside via output transmission lines. The differential amplifier has a differential pair in which emitters of a pair of transistors are connected via first and second resistors and a series circuit in which a third resistor is connected to one end of a first capacitor and a fourth resistor is connected to the other end of the first capacitor. The input terminal is coupled to the differential pair through a resistor part. A connecting point where the emitter of one transistor of the differential pair and the first resistor are connected, and a connecting point where the emitter of the other transistor of the differential pair and the second resistor are connected, are connected through the series circuit. 
     According to one embodiment of the present invention, an optical modulator driver that enhances a common-mode rejection ratio in a high frequency region and performs liner amplification suitable for pulse amplitude modulation can be provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating a structure of an optical transmitter using an optical modulator driver according to an embodiment; 
         FIG. 2  is a schematic diagram illustrating an optical modulator driver according to the related art; 
         FIG. 3  is an input-to-output characteristic for explaining linear amplification of the optical modulator driver; 
         FIG. 4  is a block diagram for explaining that common-mode components are included in a differential input signal of the optical modulator driver; 
         FIG. 5  is a schematic diagram illustrating a differential amplifier according to the related art; 
         FIG. 6  is an equivalent circuit of a current source of the differential amplifier illustrated in  FIG. 5 ; 
         FIGS. 7A, 7B  are frequency characteristics of the optical modulator driver according to the related art; 
         FIG. 8  is a schematic diagram illustrating a differential amplifier according to the embodiment of the present invention; 
         FIG. 9  is a schematic diagram illustrating an optical modulator driver according to the embodiment of the present invention; 
         FIG. 10  is a diagram illustrating voltage gain of the optical modulator driver according to the embodiment of the present invention; 
         FIG. 11  is a diagram illustrating a common-mode rejection ratio of the optical modulator driver according to the embodiment of the present invention; 
         FIG. 12  is a schematic diagram illustrating a modification of the differential amplifier according to the embodiment of the present invention; and 
         FIG. 13  is a schematic diagram illustrating another modification of the differential amplifier according to the embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, specific examples of an optical modulator driver and a differential amplifier according to an embodiment of the present invention will be described with reference to the drawings. However, the present invention is not limited to an exemplary form and various changes and modifications can be made without departing from the scope of the present invention. In description of the drawings, the same elements are denoted with the same reference numerals and overlapped explanation is omitted. 
       FIG. 8  illustrates a circuit structure of a differential amplifier Amp 1  according to an embodiment of the present invention.  FIG. 9  illustrates a structure of an optical modulator driver  100  according to the embodiment of the present invention. The optical modulator driver  100  is a travelling wave amplifier (TWA). The differential amplifier Amp 1  corresponds to each of Cells (Cell- 1  to Cell- 4 ) illustrated in  FIGS. 2, 5  and the optical modulator driver  100  according to the embodiment uses the differential amplifier Amp 1  according to the embodiment, instead of each Cell illustrated in  FIG. 2 . The differential amplifier Amp 1  includes a differential input terminal Da, a differential pair Db, an emitter follower Dc to drive the differential pair Db, two cascade transistors (transistors Tr 5 , Tr 6 ) connected to respective collectors of the differential pair Db, a current source Is, a differential output terminal Dd, a series circuit Df, and a resistor part Rp. The differential amplifier Amp 1  is further provided with the resistor part Rp and the series circuit Df, with respect to a circuit structure of a circuit example of the Cell illustrated in  FIG. 5 . 
     The differential input terminal Da includes a positive-phase input terminal Cell-in and a negative-phase input terminal Cell-inb. The differential output terminal Dd includes a positive-phase output terminal Cell-out and a negative-phase output terminal Cell-outb. A pair of positive-phase input signal and negative-phase input signal that have phases opposite to each other is input to the positive-phase input terminal Cell-in and the negative-phase input terminal Cell-inb. An amplified differential input signal is output as a pair of positive-phase output signal and negative-phase output signal that have phases opposite to each other, from the positive-phase output terminal Cell-out and the negative-phase output terminal Cell-outb. Respective polarities of the differential input signal and the differential output signal are determined according to a structure of an optical transmitter used in the optical modulator driver  100 , such that the polarities are equal to each other or are inverted to each other. The polarity of the differential signal can be easily inverted by switching the two signals constituting the differential signal. 
     The resistor part Rp includes a resistor Rb 11  (fifth resistor) and a resistor Rb 12  (sixth resistor). The negative-phase input terminal Cell-inb and the transistor Tr 3  of the differential pair Db are connected via the resistor Rb 11 . The positive-phase input terminal Cell-in and a transistor Tr 4  of the differential pair Db are connected via the resistor Rb 12 . In detail, the resistor Rb 11  is provided between the negative-phase input terminal Cell-inb and base of a transistor Tr 11  of the emitter follower Dc. The resistor Rb 12  is provided between the positive-phase input terminal Cell-in and base of a transistor Tr 12  of the emitter follower Dc. 
     The emitter follower Dc includes the transistor Tr 11 , the transistor Tr 12 , a resistor R 5 , and a resistor R 6 . The base of the transistor Tr 11  is connected to the negative-phase input terminal Cell-inb via the resistor Rb 11 . Collector of the transistor Tr 11  is connected to a power supply Vcc. Emitter of the transistor Tr 11  is grounded via the resistor R 5 . The emitter of the transistor Tr 11  is connected to base of the transistor Tr 3  of the differential pair Db. The base of the transistor Tr 12  is connected to the positive-phase input terminal Cell-in via the resistor Rb 12 . Collector of the transistor Tr 12  is connected to the power supply Vcc. Emitter of the transistor Tr 12  is grounded via the resistor R 6 . The emitter of the transistor Tr 12  is connected to base of the transistor Tr 4  of the differential pair Db. 
     The differential pair Db is comprised of a pair of circuits, one of the circuits including the transistor Tr 3  and the resistor R 1  (first resistor), the other of the circuits including the transistor Tr 4  and the resistor R 2  (second resistor). In the differential pair Db, respective emitters of the transistors Tr 3 , Tr 4  are connected to each other via the resistors R 1 , R 2 . The base of the transistor Tr 3  is connected to the emitter of the transistor Tr 11 . The emitter of the transistor Tr 3  is connected to the resistor R 1  at a connecting point P 1 . The emitter of the transistor Tr 3  is connected to the current source Is via the resistor R 1 . Collector of the transistor Tr 3  is connected to emitter of the transistor Tr 5 . The base of the transistor Tr 4  is connected to the emitter of the transistor Tr 12 . The emitter of the transistor Tr 4  is connected to the resistor R 2  at a connecting point P 2 . The emitter of the transistor Tr 4  is connected to the current source Is via the resistor R 2 . The collector of the transistor Tr 4  is connected to the emitter of the transistor Tr 6 . 
     The transistors Tr 5 , Tr 6  are provided to keep impedance of the differential output terminal Dd high. The base of the transistor Tr 5  is connected to the base of the transistor Tr 6 . The base of each of the transistors Tr 5 , Tr 6  is grounded via a capacitor C 1 . The collector of the transistor Tr 5  is connected to the positive-phase output terminal Cell-out. The collector of the transistor Tr 6  is connected to the negative-phase output terminal Cell-outb. The transistors Tr 5 , Tr 6  may be omitted and the collectors of the differential pair Db may be connected directly to the positive-phase output terminal Dout and the negative-phase output terminal Doutb, respectively. 
     The series circuit Df includes a resistor Rf 11  (third resistor), a capacitor Cf 1  (first capacitor), and a resistor Rf 2  (fourth resistor). In the series circuit Df, the resistor Rf 1  is connected to one end of the capacitor Cf 1  and the resistor R 2  is connected to the other end of the capacitor Cf 1 . The series circuit Df is connected between the connecting points P 1 , P 2 . The resistor Rf 1 , the capacitor Cf 1 , and the resistor Rf 2  are connected in series in this order. The resistor Rf 1  is connected to the emitter of the transistor Tr 3  at the connecting point P 1 . The resistor Rf 1  is provided between the emitter of the transistor Tr 3  and the capacitor Cf 1 . The resistor R 12  is connected to the emitter of the transistor Tr 4  at the connecting point P 2 . The resistor Rf 2  is provided between the emitter of the transistor Tr 4  and the capacitor Cf 1 . 
     If resistance of the resistor Rf 1  is set to rf 1 , resistance of the resistor Rf 2  is set to rf 2 , resistance of the resistor Rb 11  is set to rb 11 , a resistance of the resistor Rb 12  is set to rb 12 , and capacitance of the capacitor Cf 1  is set to cf 1 , these values satisfy the following condition: 0&lt;rf 1 , rf 2 ≦50 [Ω]; 10≦cf 1 ≦300 [fF]; and 10≦rb 11 , rb 12 ≦200 [Ω]. If the resistance of the resistor R 1  is set to r 1  and the resistance of the resistor R 2  is set to r 2 , r 1  and r 2  should be equal to each other. In addition, a lower limit of rf 1  is about 3 [Ω] and lower limits of r 1  and r 2  are about 3 [Ω]. 
     The current source Is includes a transistor Tr 7 , a resistor R 7 , and a capacitor C 2 . One end of the current source Is is connected to a connecting point P 3  of the resistors R 1 , R 2 . The current source Is is connected to the differential pair Db and provides a current to the differential pair Db. Base of the transistor Tr 7  is connected to a voltage terminal Vcon. The base of the transistor Tr 7  is grounded via the capacitor C 2 . Emitter of the transistor Tr 7  is grounded via the resistor R 7 . Collector of the transistor Tr 7  is connected to the emitter of the transistor Tr 3  via the resistor R 1  and is connected to the emitter of the transistor Tr 4  via the resistor R 2 . The capacitor C 2  restrains high-frequency oscillation of voltage potential applied to base of the transistor Tr 7 . By adjusting a direct-current (DC) voltage applied from the outside to the voltage terminal Vcon, the magnitude of a collector current of the transistor Tr 7  can be changed. The collector current becomes a current provided by the current source Is. That is, the transistor Tr 7  operates as a voltage-controlled current source. 
     One end of the resistor R 4  is connected to the power supply Vcc and one end of the resistor R 3  is grounded. The other end of the resistor R 4  is connected to the other end of the resistor R 3 . That is, the resistors R 3 , R 4  are connected in series between the power supply Vcc and a ground. The resistors R 3 , R 4  are names given to distinguish two resistors and the names thereof may be switched. A connecting point of the resistors R 4 , R 3  is connected to the base of the transistor Tr 5  and the base of the transistor Tr 6 . The resistors R 3 , R 4  constitute a so-called voltage divider that adjusts the voltage potential applied to the base of each of the transistors Tr 5 , Tr 6  by changing a ratio of respective resistances. 
     Advantages of the optical modulator driver  100  that includes the differential amplifier Amp 1  having the structure described above are illustrated in  FIGS. 10, 11 . A curve Ac 1  (comparative example 1) of  FIG. 10  shows the same simulation results as a curve Ac 1  of  FIG. 7A  and a curve Ad 1  (comparative example 1) of  FIG. 10  shows the same simulation results as a curve Ad 1  of  FIG. 7A . A curve Ac 2  (comparative example 2) of  FIG. 10  shows simulation results for Ac obtained using a circuit obtained by removing the series circuit Df from the differential amplifier Amp 1 , that is, a circuit obtained by adding only the resistor part Rp to a circuit illustrated in  FIG. 5 . Likewise, a curve Ad 2  (comparative example 2) of  FIG. 10  shows simulation results for Ad obtained using the circuit obtained by removing the series circuit Df from the differential amplifier Amp 1 , that is, the circuit obtained by adding only the resistor part Rp to the circuit illustrated in  FIG. 5 . A curve Ac 3  (embodiment) of  FIG. 10  illustrates simulation results for Ac obtained using the differential amplifier Amp 1 . A curve Ad 3  (embodiment) of  FIG. 10  illustrates simulation results for Ad obtained using the differential amplifier Amp 1 . A curve Cr 1  (comparative example 1) of  FIG. 11  shows the same simulation results as a curve Cr 1  of  FIG. 7B . A curve Cr 2  (comparative example 2) of  FIG. 11  shows simulation results obtained using the circuit obtained by removing the series circuit Df from the differential amplifier Amp 1 , that is, the circuit obtained by adding only the resistor part Rp to the circuit illustrated in  FIG. 5  and shows a CMRR calculated using a formula 1, from the curves Ac 2 , Ad 2  of  FIG. 10 . A curve Cr 3  (embodiment) of  FIG. 11  shows simulation results obtained using the differential amplifier Amp 1  and shows a CMRR calculated using the formula 1, from the curves Ac 3 , Ad 3  of  FIG. 10 . 
     For example, in the case of a symbol rate of 32 Gbaud, an improvement effect of the CMRR is obtained in a frequency range of 10 to 30 [GHz]. As illustrated in  FIG. 11 , in the curve Cr 3  according to the embodiment, an improvement effect of a maxim of 2 [dB] is obtained as compared with the curve Cr 1  according to the comparative example 1. From the frequency range, in the curve Cr 1  according to the comparative example 1, if the frequency exceeds 5 [GHz], the CMRR becomes gradually smaller than 12 [dB]. However, in the curve Cr 3  according to the embodiment, the CMRR becomes 12 [dB] or more up to a frequency of about 22 [GHz] and the frequency range is greatly extended. 
     The advantages according to this embodiment of the present invention is explained with referring the characteristics of Ad, Ac illustrated in  FIG. 10 , on the basis of the formula 1. That is, for the curves Ac 1 , Ad 1  according to the comparative examples, common-mode voltage gain Ac 1  gradually increases with increase of frequency at 10 [GHz] or more as compared with the differential voltage gain Ad 1 , because the impedance Zc 2  acts as parasitic impedance of collector of the current source Is Accordingly, the CMRR Cr 1  decreases with increase of frequency, as the ratio Ad 1 /Ac 1  decreases in the formula 1. Use of the resistor part Rp inserted between the differential input terminal Da and the differential pair Db restrains both Ac, Ad (correspond to the curves Ac 2 , Ad 2  according to the comparative example 2). In this situation, the CMRR (Cr 2 ) is degraded as compared with the comparative example 1 (Cr 1 ). However, The embodiment of the present invention provide the series circuit Df in the differential amplifier for applying positive feedback, so that only Ad is improved while Ac is still constrained, and the CMRR is improved (correspond to the curves Ac 3 , Ad 3  in  FIG. 10  and Cr 3  in  FIG. 11  according to the embodiment). 
     For the linear amplification, flatness (within variation±2 [dB] as a practical standard) of Ad is necessary. Such flatness of Ad is sufficiently satisfied by providing the series circuit Df with the resistor part Rp. 
     (Modification) 
       FIG. 12  illustrates a structure of a differential amplifier Amp 2  according to a first modification of the differential amplifier Amp 1 . The differential amplifier Amp 2  according to the first modification illustrated in  FIG. 12  is different from the differential amplifier Amp 1  according to the embodiment in that a capacitor C 3  and a capacitor C 4  are provided between the resistor part Rp and the emitter follower Dc. A low-pass filter Lp 1  is constituted of the resistor part Rp, the capacitor C 3 , and the capacitor C 4  (that is, instead of the resistor part Rp, the low-pass filter Lp 1  is provided in the differential amplifier Amp 1 ). The low-pass filter Lp 1  includes two low-pass filters, that is, a low-pass filter (first low-pass filter) having the resistor Rb 11  and the capacitor C 3 , and a low-pass filter (second low-pass filter) having the resistor Rb 12  and the capacitor C 4 . The negative-phase input terminal Cell-inb and the transistor Tr 3  of the differential pair Db are connected to each other via the low-pass filter having the resistor Rb 11  and the capacitor C 3 . The positive-phase input terminal Cell-in and the transistor Tr 4  of the differential pair Db are connected to each other via the low-pass filter having the resistor Rb 12  and the capacitor C 4 . One end of the capacitor C 3  is connected to the resistor Rb 11  and the base of the transistor Tr 11 , and the other end of the capacitor C 3  is grounded. One end of the capacitor C 4  is connected to the resistor Rb 12  and the base of the transistor Tr 12 , and the other end of the capacitor C 4  is grounded.  FIG. 13  illustrates a structure of a differential amplifier Amp 3  according to a second modification of the differential amplifier Amp 1 . 
     The differential amplifier Amp 3  according to the second modification illustrated in  FIG. 13  is different from the differential amplifier Amp 1  according to the embodiment in that the resistor part Rp is not provided and a low-pass filter Lp 2  is provided between the emitter follower Dc and the differential pair Db. The low-pass filter Lp 2  includes capacitors C 5 , C 6  and resistors R 8 , R 9 . The low-pass filter Lp 2  includes two low-pass filters, that is, a low-pass filter (third low-pass filter) having the resistor R 8  and the capacitor C 5 , and a low-pass filter (fourth low-pass filter) having the resistor R 9  and the capacitor C 6 . The negative-phase input terminal Cell-inb and the transistor Tr 3  of the differential pair Db are connected to each other via the low-pass filter having the resistor R 8  and the capacitor C 5 . The positive-phase input terminal Cell-in and the transistor Tr 4  of the differential pair Db are connected to each other via the low-pass filter having the resistor R 9  and the capacitor C 6 . The resistor R 8  is provided between the emitter of the transistor Tr 11  and the base of the transistor Tr 3 , and the base of the transistor Tr 3  is grounded via the capacitor C 5 . The resistor R 9  is provided between the emitter of the transistor Tr 12  and the base of the transistor Tr 4 , and the base of the transistor Tr 4  is grounded via the capacitor C 6 . 
     In the first and second modifications, it is confirmed that the same advantages (advantages corresponding to the curved lines Ac 3 , Ad 3 , and Cr 3 ) as the differential amplifier Amp 1  according to the embodiment illustrated in  FIGS. 9, 10  are achieved. Therefore, similar to the differential amplifier Amp 1  according to the embodiment of the present invention, the CMRR has been improved using the low-pass filter Lp 1  and the series circuit Df as in the differential amplifier Amp 2  according to the first modification and using the low-pass filter Lp 2  and the series circuit Df as in the differential amplifier Amp 3  according to the second modification.