Abstract:
A transimpedance amplifier (TIA) circuit comprises a first operational transconductance amplifier (OTA) having an input and an output. A second OTA has an input and an output. A third OTA has an input that communicates with the output of the first OTA and an output that communicates with the input of the second OTA. A first feedback path communicates with the input and the output of the first OTA and that includes a first resistor. A second feedback path communicates with the input and the output of the second OTA and that includes a first resistance. A third feedback path communicates with the input of the first OTA and the output of the second OTA.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation of U.S. patent application Ser. No. 11/294,949, filed on Dec. 6, 2005 now U.S. Pat. No. 7,116,164, which a continuation of U.S. patent application Ser. No. 10/814,534, filed on Mar. 31, 2004 now U.S. Pat. No. 7,023,271. The disclosure of the above application is incorporated herein by reference. 

   FIELD OF THE INVENTION 
   The present disclosure relates to transimpedance amplifiers, and more particularly to a transimpedance amplifier having a relatively constant bandwidth at different gain levels. 
   BACKGROUND OF THE INVENTION 
   The statements in this section merely provide background information related to the present disclosure and may not constitute prior art. 
   Operational amplifiers (opamps) are used in many different types of circuits including preamplifiers, variable gain amplifiers and the like. Referring now to  FIG. 1A , an amplifier  20  includes an opamp  24  and a feedback path  28  that couples an output of the opamp  24  to an inverting input thereof. The non-inverting input is coupled to ground or another reference potential. The amplifier  20  in  FIG. 1A  has a gain value of one. For this reason, the amplifier  20  is usually called a unity-gain amplifier or buffer. 
   Referring now to  FIG. 2A , an amplifier  30  is shown that is similar to the unity-gain amplifier  20  in  FIG. 1A . However, in the amplifier  30 , a resistance R is provided in the feedback path  28 . Another resistance R is connected between an input of the amplifier  30  and the inverting input of the opamp  24 . The amplifier  30  has a gain value of two. 
   The most relevant characteristics of an amplifier circuit are usually gain and bandwidth. In order to derive the bandwidth, an open loop response technique is used. The technique of looking at the open loop response provides information relating to the bandwidth and maximum achievable bandwidth of an amplifier circuit. 
   The DC gain of the open loop response is determined by opening the feedback loop and attaching a voltage source to an input side of the opened feedback loop. The output voltage is sensed at an output side of the opened feedback loop. Open loop response versions of the circuits in  FIGS. 1A and 2A  are shown in  FIGS. 1B and 2B . To derive the bandwidth, the DC gain of the open loop response and the first dominant pole P 1  are found. Assuming stable operation, there is only one dominant pole P 1  located below the crossover frequency. The crossover frequency is the product of the DC gain of the open loop response and the first dominant pole P 1 . The crossover frequency usually defines the bandwidth of the closed-loop amplifier. The maximum available bandwidth is related to the second non-dominant pole P 2 . 
   Referring now to  FIGS. 3A and 3B , the open loop response for the amplifiers in  FIGS. 1B and 2B  is shown, respectively. There is a constant gain from DC to a frequency of the first dominant pole P 1 . At the frequency of the pole P 1 , the gain begins falling. There is an inverse relationship between gain and bandwidth of the amplifiers  20  and  30 . In  FIG. 3A , the amplifier  20  has a gain of one. Therefore, the gain is constant until the zero crossing. In  FIG. 3B , the gain is two until the intersection with the open loop response. In general, higher gain values are associated with lower bandwidth and lower gain values are associated with higher bandwidth. The bandwidth of the amplifier  30  is approximately half of the bandwidth of the unity-gain amplifier  20  while the gain of the amplifier  30  is twice the gain of the amplifier  20 . 
   Referring now to  FIG. 4 , it may be desirable to adjust the frequency of poles P 1  and P 2  for some applications. For example, it may be desirable for the amplifier to provide a relatively constant bandwidth at different gain values. In  FIG. 4 , the gain values are relatively constant from DC up to the frequency of the first dominant pole P 1 . Because the first dominant pole P 1  is close to the second non-dominant P 2 , the gain values fall off sharply upon reaching the first dominant pole P 1 . 
   Various compensation techniques are known for adjusting the frequency of the poles of the amplifier. The opamp may be implemented using a two-stage amplifier. In two-stage amplifiers, Miller compensation and Ahuja compensation are sometimes used. Miller compensation employs a feedback capacitor connected across an input and output of the second stage amplifier. In Ahuja compensation, a current gain device is added in the feedback loop of the second stage amplifier. Another compensation technique is used in folded cascode circuits that are output compensated. Specifically, a capacitor is coupled to an output of the circuit. 
   Referring now to  FIGS. 3A ,  3 B and  5 , it is difficult to adjust the frequencies of the poles P 1  and P 2  shown in  FIGS. 3A and 3B  without creating stability problems. In  FIG. 5 , the phase response that is associated with the open loop responses of  FIGS. 3A and 3B  is shown. The phase response is 180 degrees from DC to about the frequency of the first pole P 1 . At the frequency of pole P 1 , the phase response is approximately 90 degrees. The phase response remains at 90 degrees from the frequency of the first dominant pole P 1  until about the frequency of the second non-dominant pole P 2 . At the frequency of the second non-dominant pole P 2 , the phase response is approximately zero degrees. 
   The phase response in  FIG. 5  also illustrates a phase margin of approximately 90 degrees. The phase margin is usually defined at unity gain. For acceptable stability, the phase margin should be greater than approximately 55–60 degrees otherwise oscillation will occur. Therefore, the 90 degree phase margin that is shown in  FIG. 5  is typically acceptable. However, moving the frequency of the second non-dominant pole P 2  closer to the zero crossing will reduce the phase margin. At some point, this will cause oscillation. Conversely, moving the first dominant pole P 1  closer to the zero crossing in  FIGS. 3A and 3B  will increase the phase margin. At some point, this too will cause oscillation. For these reasons, it is generally not possible to adjust the frequencies of the poles P 1  and P 2  shown in  FIGS. 3A and 3B  to produce the open loop response of  FIG. 4  without creating stability problems. 
   Referring now to  FIGS. 6A and 6B , a transimpedance amplifier (TIA)  60  includes an opamp  64  having a transconductance value (−g m ). The opamp  64  has a feedback resistor (R f )  66 . A capacitance (C 1 )  70  is connected between an input of the TIA  60  and ground or a reference potential. Another capacitance (C 2 )  72  and a load resistance (R L )  74  are connected between the output of the TIA  60  and ground or a reference potential. An input  76  to the TIA  60  is a current I and an output  80  of the TIA  60  is a voltage V. 
   Referring now to  FIG. 7 , the open loop response for the TIA  60  in  FIG. 6B  is shown. At DC, the gain is equal to g m R L . If we assume that the capacitance C 1  is much greater than the capacitance C 2  and the resistance R f  is large, the frequency of the first dominant pole P 1 =1/(C 1 R f ). Further, the frequency of the second non-dominant pole P 2 =1/(C 2 *(R L  in parallel with R f )). The zero crossing occurs at a frequency of (g m R L )/(C 1 R f ). 
   Referring now to  FIG. 8 , the closed loop response for the TIA  60  is shown. Two different gain curves are illustrated in  FIG. 8 . One curve corresponds to the resistance R f =R f1  and the other curve corresponds to the resistance R f =R f2 , where R f2 &gt;R f1 . For a given value of R f , higher gain is associated with lower bandwidth and lower gain is associated with higher bandwidth. 
   SUMMARY OF THE INVENTION 
   A transimpedance amplifier (TIA) circuit according to the present invention includes a first opamp having an input and an output. A second opamp has an input that communicates with the first opamp and an output. A first feedback path communicates with the input and the output of the first opamp and includes a first resistance. A second feedback path communicates with the input and the output of the second opamp and includes a second resistance. A third feedback path communicates with the input of the first opamp and the output of the second opamp. 
   In other features, the first feedback path includes a first capacitance in parallel with the first resistance. The second feedback path includes a second capacitance in parallel with the second resistance. The first feedback path further includes a third resistance in series with the first resistance and the first capacitance. The third resistance has a resistance value that is approximately two times a resistance value of the first resistance. The first and third resistances have substantially equal resistance values. The second feedback path further includes a fourth resistance in series with the second resistance and the second capacitance. The fourth resistance has a resistance value that is approximately two times a resistance value of the second resistance. The second and fourth resistances have substantially equal resistance values. The first and second capacitances have substantially equal capacitance values. 
   In other features, a third opamp has an input that communicates with the output of the first opamp and an output that communicates with the input of the second opamp. The third feedback path includes a fifth resistance. Third, fourth and fifth capacitances have one end that communicates with the inputs of the first, second and third opamps, respectively. A sixth capacitance communicates with the output of the second opamp. 
   In other features, a preamplifier comprises the TIA circuit. A hard disk drive comprises the preamplifier. A variable gain amplifier comprises the TIA circuit. A read channel circuit comprises the variable gain amplifier. 
   Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 
   Further areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein: 
       FIGS. 1A and 2A  are electrical schematics of amplifier circuits according to the prior art; 
       FIGS. 1B and 2B  are electrical schematics of the circuits of  FIGS. 1A and 2A  in an open loop response configuration; 
       FIGS. 3A and 3B  are graphs illustrating the open loop responses of the amplifiers of  FIGS. 1B and 2B ; 
       FIG. 4  is a graph illustrating a desired closed loop gain response for the amplifiers of  FIGS. 1A and 2A ; 
       FIG. 5  is a graph illustrating the phase response corresponding to the open loop response of  FIGS. 3A and 3B ; 
       FIGS. 6A and 6B  are electrical schematics of TIA circuits according to the prior art in closed loop and open-loop response configurations; 
       FIG. 7  is a graph illustrating the open loop gain response for the TIA of  FIG. 6B ; 
       FIG. 8  is a graph illustrating the open loop gain response of the TIA of  FIG. 6  for two different values of a resistance R f ; 
       FIG. 9  is an electrical schematic of a multi-stage TIA according to the present invention; 
       FIG. 10  is a graph illustrating the open loop response for the TIA of  FIG. 9 ; 
       FIG. 11  is a graph illustrating the gain of the TIA of  FIG. 9  as a function of a resistance R f ; 
       FIGS. 12A and 12B  are electrical schematics of a variable-gain constant-bandwidth TIA according to the present invention; 
       FIG. 13  is a graph of the gain of the TIA of  FIG. 12  as a function of a resistance R f ; 
       FIG. 14  is a graph of the closed loop gain of the TIA of  FIG. 12 ; 
       FIGS. 15A and 15B  illustrate the gain of the TIA of  FIG. 12  at low frequency and high frequency, respectively; 
       FIG. 16  illustrates the TIA of  FIG. 12  in a preamplifier of a hard disk drive system; and 
       FIG. 17  illustrates the TIA of  FIG. 12  in a variable gain amplifier of a read channel circuit. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. For purposes of clarity, the same reference numbers will be used in the drawings to identify similar elements. 
   Referring now to  FIG. 9 , a multi-stage TIA  90  converts an input current I at  92  into an output voltage V at  94 . The TIA  90  includes a first opamp  96 , a second opamp  98  and a third opamp  100  that are coupled in series between the input and the output of the TIA  90 . The opamps  96 ,  98  and  100  have transconductance values −g m1 , −g m2  and −g m3 , respectively. A resistance (R 1 )  104  is connected between the input and the output of the first opamp  96 . Another resistance (R 3 )  106  is connected between the input and the output of the third opamp  100 . A resistance (R f )  108  is connected between the input and the output of the TIA  90 . Capacitors and/or capacitances C 1 , C 2 , and C 3  ( 109 ,  110 , and  112 , respectively) are coupled between the inputs of opamps  96 ,  98 , and  100 , respectively, and ground (or another reference potential). Additionally, a capacitor and/or capacitance (C 4 )  960  is coupled between the output of the TIA  90  and ground (or another reference potential). 
   Referring now to  FIG. 10 , the open loop response of the TIA  90  is shown. The resistance R f &gt;&gt;1/g m1  and the gain produced by the first opamp  96  is R 1 /R f . Additionally, g m1 /C 1 ≈g m1 /C 2 ≈g m3 /C 3 ≈g m3 /C 4  such that the poles produced by the capacitors C 1 –C 4  are closely spaced. There is no dominant pole. The DC gain is equal to (R 1 /R f )g m2 R 3 . This gain value remains relatively constant until the closely spaced pole frequencies. At those frequencies, the gain falls off sharply, as shown in  FIG. 10 .  FIG. 10  illustrates a nearly constant bandwidth for a range of gain values. However, given the above assumptions regarding the gain parameters and capacitor values, the TIA  90  may experience phase margin problems when operating above unity gain. 
   Referring now to  FIG. 11 , it is possible to operate the TIA  90  below unity gain using high values of the resistance R f . However, limited gain variation can be realized. This is illustrated in  FIG. 11 , where the gain is shown as a function of the resistance R f . When the value of resistance R f  is infinite, the gain is equal to R 1 g m2 R 3 . When R f =R 1 g m2 R 3 , the gain is unity. When it is above this value, the gain cannot be varied much and the circuit is stable. When R f &lt;R 1 g m2 R 3 , the gain can be varied but the circuit is unstable. 
   Referring now to  FIGS. 12A ,  12 B,  15 A and  15 B, a TIA  150  according to one embodiment of the present invention is shown. The TIA  150  includes a feedback path  154  that communicates with the input and the output of the opamp  96 . In  FIG. 12A , the feedback path  154  has a resistance that decreases as frequency increases. For example and referring now to  FIG. 12B , the feedback path  154  can include a resistor R 1a    158  connected in series with the parallel combination of a resistor R 1b    162  and a capacitor and/or capacitance (C P1 )  166 . At low frequencies, the capacitor  166  is essentially an open circuit and the resistance of the feedback path  154  is essentially R 1 =R 1a +R 1b . At high frequencies, the capacitor  166  shunts the resistor  162  and the resistance of the feedback path  154  is essentially R 1a . The combination of resistances R 1a  and R 1b  and the capacitance C P1  provide a variable resistance that decreases with increases in frequency. 
   The TIA  150  further includes a feedback path  170  that communicates with the input and the output of the opamp  100 . In  FIG. 12A , the feedback path  170  has a resistance that decreases with increases in frequency. For example and referring now to  FIG. 12B , the feedback path  170  includes a resistor R 3a    172  connected in series with the parallel combination of a resistor R 3b    173  and a capacitor and/or capacitance (C P3 )  174 . While a combination of resistances and capacitances are shown, any other suitable techniques for providing a variable resistance may be used. For example, transistors can be used to short resistances and conventional approaches may be used. At low frequencies, the capacitor  174  is essentially an open circuit and the resistance of the feedback path  170  is essentially R 3 =R 3a +R 3b . At high frequencies, the capacitor  174  shunts the resistor  173  and the resistance of the feedback path  170  is essentially R 3a . The effect of this resistive transition is shown in  FIGS. 15A and 15B . Likewise, the combination of resistances R 3a  and R 3b  and the capacitance C P3  provide a variable resistance that decreases with increasing frequency. 
   Referring now to  FIG. 13 , the gain response for the TIA  150  is shown as a function of the resistance R f . A maximum gain equal to R 1 g m2 R 3  can be produced at DC. A minimum gain equal to R 1 g m2 R 3 /9 can be produced at frequencies greater than 3/C P1 R 1  and 3/C P3 R 3  when R 3a =2R 3b  and R 1a =2R 1b . Between these maximum and minimum gain levels, a linear gain variation region exists. Within the linear gain variation region, a desired above-unity gain level can be obtained by choosing an appropriate value of the resistance R f . 
   Referring now to  FIG. 14 , the gain of the TIA  150  is shown for different values of resistance R f1 , R f2 , R f3 , and R f4 . Assuming g m1 /C 1 ≈g m1 /C 2 ≈g m3 /C 3 ≈g m3 /C 4 , the non-dominant poles produced by capacitors C 1 –C 4  are closely spaced. Therefore, each gain curve is relatively constant until reaching the closely spaced pole frequencies. At those higher frequencies, the gain falls off sharply. Thus, varying the gain of the TIA  150  (by varying the resistance R f ) produces only minimal variation in bandwidth. 
   Further, by choosing suitable transconductance and capacitance values, the poles of the TIA  150  are closely spaced at high frequencies. Therefore, the TIA  150  has a relatively constant bandwidth up to the non-dominant pole frequencies. At those frequencies, the gain drops off rapidly. 
   It should be understood that various values can be selected for the transconductance values g m1 , g m2 , and g m3 . For example, the same transconductance value can be used for all of the opamps  96 ,  98  and  100 . Alternatively, each transconductance value can be different than one or more other transconductance values. For example, a larger value of g m1  can be used for input noise or input impedance purposes. Further, a larger value of g m3  can be used for output impedance purposes. However, it should be understood that other transconductance values can be used without departing from the scope of the invention. 
   Similarly, resistances R 1a , R 1b , R 3a , and R 3b , as well as capacitances C 1 , C 2 , C 3 , C 4 , C P1  and C P3 , can be selected as desired for any given application of the invention. For example, resistors  158  and  172  can be twice as large as resistors  162  and  173 , respectively, and the values of capacitors C P1  and C P3  can be the same. However, other resistance and capacitance values can be used without departing from the teachings of the present invention. For some preferred embodiments, the value of resistors  158 ,  162 ,  172 , and  173  are the same. In some embodiments, the transistors in the op-amps are CMOS transistors. 
   Referring now to  FIGS. 16 and 17 , various exemplary applications are shown. In  FIG. 16 , the TIA  150  according to the present invention is employed by a preamplifier  200  of a hard disk drive system  210 . In  FIG. 17 , the TIA  150  is implemented in a variable gain amplifier (VGA)  220  of a read channel circuit. Skilled artisans will appreciate that the TIA is suitable for other applications requiring a relatively constant bandwidth at various above-unity gain levels. 
   As can be appreciated, the TIA circuit according to the present invention provides constant bandwidth over a wide range of gain values. For example, one implementation provides a gain range of 5–50 or greater. Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.