Updated March 15, 2012.  See Document History at end for details.

# One-Bend Amplifier

Part 2: Improving important details of a current-feedback amplifier

### Introduction

I last said in the previous article that the one-bend amplifier was likely unfinished.  When I did a slew rate analysis,  I found it to be 3V/µs.   Consider the following slew rate calculations:

 (1) vpk = 2PR = 2 × 30W × 8Ω = 21.91V

 (2) minimum slew rate = 2πfvpk = 2π × 20kHz × 21.91V = 2.753V/µs

In this case 3V/µs was inadequate for a this minimum calculated slew rate of 2.753V/µs.  As a result the Fourier results for 20kHz at full power were very bad for the original one-bend circuit.

SPICE Model of Power Supply (for all circuits).

### Improving Slew Rate

I deemed two improvements were necessary to remedy the problem with slew rate.  Slew rate was worst on pull than push.  To improve the pull, I added a current source in parallel with the resistor loading stage 1.  Then because slew is a matter of limited current driving capacitance, I increased the bias for stages 1 and 2:  stage 1 from 1mA to 10mA, and stage 2 from 45mA to 119mA.   The 119mA bias was to dissipate 4W per M1 and M2 based on full utilization of common 5W TO220 heat sinks.  In the first stage, I paired the JFETs and specified the higher current rated C version to give current margin over the new 10mA bias.  To simplify setup, I changed the adjustable M2 MOSFET current source to one fixed by the stable VBE voltage of an NPN transistor.  The result is the following circuit.

 Figure 1:  Current-feedback amplifier corrected for higher slew rate SPICE Model

 Figure 2:  Slew rate analysis shows dv/dt of 5.2V/µs good for 37.77kHz power bandwidth

Fourier analysis at 1kHz for vout:
No. Harmonics: 16, THD: 0.0012549 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels -------- --------- --------- --------- --------- --------- 1 1000 21.8095 1 100 0 2 2000 0.000258371 1.18467E-05 0.00118467 -98.5281 3 3000 0.000058014 2.66003E-06 0.000266003 -111.502 4 4000 0.000039892 1.82911E-06 0.000182911 -114.755 5 5000 3.77342E-05 1.73017E-06 0.000173017 -115.238 6 6000 1.46938E-05 6.73733E-07 6.73733E-05 -123.430 7 7000 3.41571E-05 1.56615E-06 0.000156615 -116.103 8 8000 2.11585E-06 9.70147E-08 9.70147E-06 -140.263 9 9000 9.57353E-06 4.38961E-07 4.38961E-05 -127.151 10 10000 8.64029E-06 3.9617E-07 0.000039617 -128.042 11 11000 6.54572E-06 3.00131E-07 3.00131E-05 -130.454 12 12000 7.97776E-06 3.65792E-07 3.65792E-05 -128.735 13 13000 9.20586E-06 4.22103E-07 4.22103E-05 -127.492 14 14000 2.35572E-06 1.08013E-07 1.08013E-05 -139.330 15 15000 4.34586E-06 1.99264E-07 1.99264E-05 -134.011

Although distortion is not as low as at 1kHz, Fourier analysis at 20kHz proves slew rate improvement largely successful.
No. Harmonics: 16, THD: 0.0573418 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels 1 20000 21.7961 1 100 0 2 40000 0.0056118 0.000257469 0.0257469 -71.7855 3 60000 0.00956154 0.000438682 0.0438682 -67.157 4 80000 0.000835605 3.83374E-05 0.00383374 -88.3275 5 100000 0.00464674 0.000213192 0.0213192 -73.4246 6 120000 0.00051708 2.37235E-05 0.00237235 -92.4964 7 140000 0.00266117 0.000122094 0.0122094 -78.2661 8 160000 0.000421559 1.93411E-05 0.00193411 -94.2704 9 180000 0.00154427 7.08509E-05 0.00708509 -82.9931 10 200000 0.000349586 1.60389E-05 0.00160389 -95.8965 11 220000 0.000830694 3.81121E-05 0.00381121 -88.3787 12 240000 0.000293413 1.34617E-05 0.00134617 -97.418 13 260000 0.000357373 1.63962E-05 0.00163962 -95.7051 14 280000 0.000247156 1.13395E-05 0.00113395 -98.9081 15 300000 4.02591E-05 1.84708E-06 0.000184708 -114.67

 Figure 3:  Small signal transfer error curve Figure 4:  Large signal transfer error curve The slight kink is attributable to SPICE convergence difficulties, actual curve is likely as smooth as the small signal one on the left.

 Figure 5:  Stability analysis for slew rate improved circuit.

The stability analysis show and outstanding 80 degrees of phase margin.  However, although the 1kHz dominant pole is better than one at 10Hz, one ≥ 10kHz is desired.

### Raising the Dominant Pole Frequency

By plotting the stability analysis more specifically, I determined that the 1kHz dominant pole was determined largely by the interaction between the load resistance of stage one and the Miller capacitance seen at the input of M1.  Therefore, I sought to lower the Miller capacitance by reducing the gain of the second stage.  Using a source resistor on M1 to lower the gain would also limit the positive voltage swing.  As a result I decided to add the local feedback between the drain and gate resistor of M1.  This addition changes the circuit to that of figure 6 below.  To avoid the tedium of complex calculations, I tried a 100kΩ for the new component RC and got excellent results.

 Figure 6:  Current-feedback amplifier improved for higher dominant pole. SPICE Model

 Figure 7:  Slew rate still holds at dv/dt = 5.2V/µs

Fourier analysis at 1kHz for vout:
No. Harmonics: 16, THD: 0.00624645 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels 1 1000 20.6212 1 100 0 2 2000 0.00121863 5.90959E-05 0.00590959 -84.5689 3 3000 0.000318355 1.54382E-05 0.00154382 -96.2281 4 4000 0.000184075 8.92648E-06 0.000892648 -100.986 5 5000 0.000167846 8.13948E-06 0.000813948 -101.788 6 6000 4.15484E-05 2.01483E-06 0.000201483 -113.915 7 7000 8.79902E-05 4.26697E-06 0.000426697 -107.398 8 8000 1.05453E-05 5.11378E-07 5.11378E-05 -125.825 9 9000 9.64684E-06 4.67811E-07 4.67811E-05 -126.599 10 10000 2.04371E-05 9.91068E-07 9.91068E-05 -120.078 11 11000 1.75095E-05 8.49097E-07 8.49097E-05 -121.421 12 12000 0.000011695 5.67135E-07 5.67135E-05 -124.926 13 13000 1.34944E-05 6.54395E-07 6.54395E-05 -123.683 14 14000 1.77303E-06 8.59805E-08 8.59805E-06 -141.312 15 15000 2.52197E-06 1.22299E-07 1.22299E-05 -138.252

Fourier analysis at 20kHz for vout:
No. Harmonics: 16, THD: 0.0506489 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels 1 20000 20.6027 1 100 0 2 40000 0.00374705 0.000181872 0.0181872 -74.8047 3 60000 0.00848886 0.000412027 0.0412027 -67.7015 4 80000 0.000622974 3.02376E-05 0.00302376 -90.3891 5 100000 0.00394035 0.000191254 0.0191254 -74.3678 6 120000 0.000462974 2.24716E-05 0.00224716 -92.9673 7 140000 0.00215136 0.000104422 0.0104422 -79.6242 8 160000 0.000376485 1.82736E-05 0.00182736 -94.7635 9 180000 0.00116204 5.64023E-05 0.00564023 -84.9741 10 200000 0.000309166 1.50061E-05 0.00150061 -96.4746 11 220000 0.000545727 2.64882E-05 0.00264882 -91.539 12 240000 0.000256768 1.24629E-05 0.00124629 -98.0876 13 260000 0.000147549 7.16162E-06 0.000716162 -102.9 14 280000 0.000215353 1.04527E-05 0.00104527 -99.6154 15 300000 0.000109782 5.32853E-06 0.000532853 -105.468

 Figure 8:  Stability analysis shows a dominant pole of about 23kHz

 Figure 9: Small signal transfer error curve Figure 10: Large signal transfer error curve

### Can It Be Made to Meet all Specifications?

Having lost a one-bend curve to gain a desirable dominant pole, I had to think of a change that would gain both for me without losing some other quality.  After altering the previous circuit in every possible way without avail, I decided to tap the local feedback off of the output instead of the drain of M1.  This is now actually a multiple feedback configuration.

 Figure 11:  Current-feedback amplifier improved for higher dominant pole SPICE Model

Since I chose RC for the desired dominant pole in the process of making the circuit change, I was most eager to see the transfer curves.  They turned out well with R15 and R16 set at 1.8kΩ for somewhat low second stage gain.  The open-loop stability analysis showed a dominant pole slightly above my 10kHz target with 82 degrees of phase margin.  Last of all, I verified that slew rate was not lost in perfecting the other qualities.

 Figure 12:  Small signal transfer error curve Figure 13:  Large signal transfer error curve The slight kink in the large signal curve is attributable to SPICE convergence difficulties; the small signal one on the left shows a nice smooth curve in the same range.

Fourier analysis at 1kHz for vout:
No. Harmonics: 16, THD: 0.016281 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels 1 1000 21.1525 1 100 0 2 2000 0.00343828 0.000162547 0.0162547 -75.7804 3 3000 0.000172863 8.1722E-06 0.00081722 -101.753 4 4000 5.42204E-05 2.5633E-06 0.00025633 -111.824 5 5000 3.67777E-05 1.73869E-06 0.000173869 -115.196 6 6000 3.36128E-05 1.58907E-06 0.000158907 -115.977 7 7000 2.07878E-05 9.82755E-07 9.82755E-05 -120.151 8 8000 1.78872E-05 8.4563E-07 0.000084563 -121.456 9 9000 0.000032523 1.53754E-06 0.000153754 -116.263 10 10000 8.33138E-06 3.93871E-07 3.93871E-05 -128.093 11 11000 2.70611E-05 1.27933E-06 0.000127933 -117.86 12 12000 6.4671E-06 3.05736E-07 3.05736E-05 -130.293 13 13000 0.000015963 7.54663E-07 7.54663E-05 -122.445 14 14000 8.20451E-06 3.87873E-07 3.87873E-05 -128.226 15 15000 5.42339E-06 2.56394E-07 2.56394E-05 -131.822

Fourier analysis at 20kHz for vout:
No. Harmonics: 16, THD: 0.066975 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels 1 20000 21.1391 1 100 0 2 40000 0.00402414 0.000190365 0.0190365 -74.4083 3 60000 0.0105682 0.000499935 0.0499935 -66.0217 4 80000 0.000838083 3.96461E-05 0.00396461 -88.036 5 100000 0.00607038 0.000287164 0.0287164 -70.8374 6 120000 0.000507738 2.40189E-05 0.00240189 -92.3889 7 140000 0.00413665 0.000195687 0.0195687 -74.1688 8 160000 0.000384928 1.82093E-05 0.00182093 -94.7941 9 180000 0.00296947 0.000140473 0.0140473 -77.0481 10 200000 0.000319767 1.51268E-05 0.00151268 -96.4051 11 220000 0.00215871 0.000102119 0.0102119 -79.8179 12 240000 0.000289091 1.36756E-05 0.00136756 -97.2811 13 260000 0.00157256 7.43912E-05 0.00743912 -82.5696 14 280000 0.000265267 1.25486E-05 0.00125486 -98.0281 15 300000 0.00113568 5.37244E-05 0.00537244 -85.3966

 Figure 14:  Open-loop stability plot shows dominant pole > 10kHz and phase margin of 82 degrees.

 Figure 15:  Slew rate drops slightly to 5.0V/µs

### Last Thoughts

The one-bend ideas seems in the end only to increase the odds of a one-bend result.  Negative feedback appears to be able to alter the transfer curve in capricious ways that are very hard to pin down.  Therefore, no presumption can be inferred about a distortion outcome with out attention to every detail.

The slew rate, though now acceptable, is still short of what most would like and perhaps still leaves the design incomplete.