Copyright © 2010 by Wayne Stegall
Updated November 2, 2010. See document history at end.
Musical Feedback Amplifiers
Introduction
I bought my first audio system at the end of the classic audio
period. That is, just before integrated circuit operational
amplifiers and CD players completely changed the audio market. I
first heard of the deficiency when my audio retailer offered to buy
back my Nakamichi 480 cassette deck. His rationale was that
Nakamichi abandoned discrete amplifiers in their decks in favor of the
new opamps. Many audiophiles were looking to buy their older
equipment because it sounded better. Are operational amplifiers
that bad? Certainly, they have improved greatly since they first
saw use in audio equipment.
The Problem
I believe that the common use of dominantpole compensation in
operational amps is the major cause of complaints of sterile or harsh
sound on the part of some audiophiles. Many amplifiers have open
loop phase shift exceeding 180° before gain drops below unity without
some form of compensation. This results in undesirable RF
oscillations. Dominantpole compensation adds extra capacitance
to one of the stages to create a lower dominant pole. Then the
gain will drop below unity before phase shift gets near enough to 180°
to cause oscillations. Consider the following openloop
characteristic of a 741 opamp, that its response falls 6db/octave
(20db/decade) above the dominant pole. This response is typical
of many opamps.
Figure 1: Open
loop gain of 741 opamp shows 10Hz dominant pole.


Distortion is typically reduced by the feedback factor (A
_{OL}/A
_{CL}).
Now
consider
the
following
distortion
suppression
plot
at
unity
closedloop
gain
(A
_{CL} = 0dB). Above the dominant pole,
the
reduction in distortion
suppression creates a distortion profile with greater distortion and
more of it consisting of high numbered harmonics. This is
contrary to musical and euphonic distortion profiles that fall quickly
with harmonic number.
Figure 2: Distortion suppression
diminishes 6db/octave above the dominant pole frequency.


The Solution
One could always revert to single stage amplifiers which never approach
180° phase shift. A three stage amplifier like the 741 would
always approach an uncompensated phase shift of at least 270°.
Two stage amplifiers ideally would approach 180° phase shift, but
reality dictates they may require compensation as well. In any
case, if the dominant pole could be made greater than 10kHz11kHz, the
distortion profile would be much flatter than in the above diagram.
In the case of the three stage amplifier, if one had access to the
compensation terminals or the design was discrete, gain could be
sacrified for a higher dominant pole frequency. This would amount
to 40db of gain out to 10kHz for a 741. The amplifier would have
more
distortion but
perhaps that more agreeable to some audiophiles (An open loop
distortion of 10% would be reduced by feedback to 0.1%). Opamps
with greater gainbandwidth products would produce better overall
results than this example.
Another tweek is a matter of preference. Symmetrical circuit
designs produce odd harmonics only. Designing in asymmetry or
adding it after the fact can bias the distortion profile back to having
a balance of even and odd harmonics. An appropriatesized
resistor or a current source from the output of an amplifier to one of
the supply rails can accomplish this. An added benefit is the
elimination of crossover distortion by rebiasing the output stage to
class A.
Two Stage Amplifier Examples
The following circuits were unstable without compensation according to
SPICE
^{1} modeling. With dominant
pole compensation of pole frequency
>= 20kHz, they showed stable results. I tried poles
approaching 100kHz with good results also. Their asymmetrical
design should ensure even and odd harmonics for those with that
preference.
The design for each proceeds as follows:
 Make transistor choices. (I chose LSK170A JFETs and 2N3906
PNPs for these analyses, other choices would work well too.)
 Decide power supply voltages.
 Choose R_{L} (and R_{1} and R_{2} if
used) for desired output impedance (in this case 1kΩ).
 Choose R_{BE} to set bias through Q_{1}.
Check Q_{1} datasheet for a proper value here.
 Choose C_{C} for desired compensation pole
frequency. (Ordinarily this involves examining the loop gain in
great detail, here SPICE should show whether our pole chosen for
musical reasons will result in oscillation.)
 Calculate maximum possible R_{S} value to choose R_{S}
potentiometer value.
 Adjust R_{S} in final circuit to trim offset in output to
0mV.
Notes:
Output impedance in calculations is openloop. Closed loop output
impedance will be reduced by the feedback factor (A
_{OL}/A
_{CL}).
Adding
a
small
resistance
(100Ω1kΩ)
on
the
output
can
give
short
circuit protection where an external cable is driven.
As for the outcomes, all had a declining harmonic profile at 1kHz, the
first two emphasizing the second harmonic. That the last
emphasized the 3rd, 6th, and 9th relative to the downward trend
suggests an unexpected symmetry to the design perhaps due to more
direct feedback to the source of the input transistor.
Figure 3: Simplest voltagefeedback opamp with noninverting
feedback network.


Design Procedure
Choose power supplies as
+15V.
Z
_{OUT} = R
_{L}  (R
_{1} + R
_{2})
= 1kΩ.
Choose R
_{L} =
2kΩ,
therefore R
_{1} + R
_{2} =
2kΩ.
For gain of 10, R
_{1} =
200Ω,
R
_{2} =
1.8kΩ. (Ideal
gain formula here is A
_{CL} = 1 + R
_{2}/R
_{1})
i
_{BQ3} = V
_{SS}/(h
_{fe} x Z
_{OUT})
= 15/(100 x 2kΩ) = 75µA.
LSK170A has min I
_{DSS} of 2.6mA, choose i
_{D} = 2mA
and calculate
R
_{BE}.
R
_{BE} = v
_{be}/(i
_{D}  i
_{BQ3})
= 700mV/(2mA  75µA) = 363.6363636Ω.
Round up to nearest standard 5% value: R
_{BE} =
360Ω.
r
_{bQ3} = V
_{T}/i
_{BQ3} = 25mV/75µA =
333.3333333Ω. (V
_{T} is the temperature dependent
characteristic voltage of a PN junction, usually 2526mV)
R
_{POLE} = R
_{BE}  r
_{bQ3} = 360Ω 
333.3333333Ω = 173.0769231Ω
C_{POLE} =

1
2πf_{POLE}R_{POLE} 
=

1
2π x 20kHz x 173.0769231Ω 
= 45.97809467nF

C
_{b} = C
_{ibo} + C
_{obo}(A+1) = 10pF +
4.5pF(1kΩ/333.3333333Ω + 1) = 28pF (These from 2N3906 datasheet,
multiplying C
_{obo} by A+1 is the Miller effect)
C
_{C} = C
_{POLE}  C
_{b}, because C
_{POLE}
>> C
_{b, }C
_{C} (approx.)= C
_{POLE} =
45.97809467nF.
Choose standard value C
_{C} =
47nF.
R
_{SMAX} = (V
_{SS}+V
_{p0MAX})/(i
_{D}
x 2) = (15V+2V)/(2 x (700mV/360Ω + 75µA)) = 4.209078404kΩ.
Choose R
_{S} =
5kΩ
potentiometer.
SPICE results: 3dB @ 721kHz, SNR = 109.9167199dB
Fourier analysis for v(vout) @1V peak:
No. Harmonics: 10, THD: 0.0325317 %, Gridsize: 200,
Interpolation Degree: 1
Harmonic 
Frequency 
Magnitude 
Phase 
Norm. Mag 
Norm. Phase 






0 
0 
0 
0 
0 
0 
1 
1000 
0.998134 
90.083 
1 
0 
2 
2000 
0.000322411 
166.06 
0.000323014 
75.972 
3 
3000 
1.9347e005 
61.106 
1.93832e005 
28.9777 
4 
4000 
2.41122e005 
161.97 
2.41573e005 
71.882 
5 
5000 
9.61602e006 
163.8 
9.63399e006 
73.716 
6 
6000 
1.99794e005 
18.9461 
2.00168e005 
109.029 
7 
7000 
2.44962e006 
25.7044 
2.4542e006 
115.788 
8 
8000 
2.00716e006 
105.38 
2.01091e006 
195.463 
9 
9000 
5.51143e006 
52.899 
5.52173e006 
37.1841 
SPICE Model for
circuit of
figure 3^{2}.
Figure 4: Simplest currentfeedback opamp with noninverting
feedback network. 

Design Procedure
The design is the same as the first circuit of
figure 3 except you may have to
tinker with more values:
Z
_{OUT} = R
_{L}  (R
_{1} + R
_{2})
Because R
_{1}  R
_{2} sets lower limit for R
_{S}
trim it was necessary to lower R
_{1} and R
_{2}.
You may
have to rechoose them yourself before recalculating. This will be
necessary if you notice that you cannot zero a persistent negative
offset. I had forgotten I had made these changes until I examined
my SPICE model. ;)
Choose R
_{L} =
2.2kΩ
To get R
_{S} to trim I chose, for gain of 10, R
_{1} =
82Ω,
R
_{2} =
750Ω.
(Ideal gain formula here is A
_{CL} = 1 + R
_{2}/R
_{1})
Z
_{OUT} = R
_{L}  (R
_{1} + R
_{2}) =
2.2kΩ  (82Ω + 750Ω) = 603.6939314Ω. (Lower than target impedance ok.)
LSK170A has min I
_{DSS} of 2.6mA, choose i
_{D} = 2mA
and calculate
R
_{BE}.
i
_{BQ3} = ((V
_{SS}/Z
_{OUT})  (R
_{1}/(R
_{1}
+ R
_{2}))i
_{D})/h
_{fe}
= (15/2.2kΩ  (82Ω/(82Ω+750Ω))2mA)/100 = 66.21066434µA. (Here R
_{1}/(R
_{1}
+ R
_{2}) is the current divider ratio for current through R
_{2})
R
_{BE} = v
_{be}/(i
_{D}  i
_{BQ3})
= 700mV/(2mA  66.21066434µA) = 361.9835869Ω.
Round to nearest standard 5% value: R
_{BE} = 360Ω.
Rechose R
_{BE} =
430Ω
to allow zeroing offset voltage in SPICE.
r
_{bQ3} = V
_{T}/i
_{BQ3} = 25mV/66.21066434µA
= 377.5826787Ω. (V
_{T} is the temperature dependent
characteristic voltage of a PN junction, usually 2526mV)
R
_{POLE} = R
_{BE}  r
_{bQ3} = 430Ω 
377.5826787Ω = 201.0451142Ω
C_{POLE} =

1
2πf_{POLE}R_{POLE} 
=

1
2π x 20kHz x 201.0451142Ω 
= 39.58189776nF

C
_{b} = C
_{ibo} + C
_{obo}(A+1) = 10pF +
4.5pF(603.6939314Ω/377.5826787Ω + 1) = 21.69477573pF (These from 2N3906
datasheet,
multiplying C
_{obo} by A+1 is the Miller effect)
C
_{C} = C
_{POLE}  C
_{b}, because C
_{POLE}
>> C
_{b, }C
_{C} (approx.)= C
_{POLE} =
39.58189776nF.
Choose standard value C
_{C} =
43nF.
R
_{SMAX} = (V
_{p0MAX})/i
_{D}  (R
_{1}
 R
_{2}) = (2V)/(700mV/430Ω + 66.21066434µA)  (82Ω  750Ω)
= 1.28065872kΩ
 73.91826923Ω = 1.20674045kΩ.
Choose R
_{S} =
1.5kΩ
potentiometer.
SPICE results: 3dB @ 344kHz, SNR = 111.5468636dB
Fourier analysis for v(vout) @1V peak:
No. Harmonics: 10, THD: 0.141913 %, Gridsize: 200, Interpolation
Degree: 1
Harmonic 
Frequency 
Magnitude 
Phase 
Norm. Mag 
Norm. Phase 
 
 
 
 
 
 
0 
0 
0 
0 
0 
0 
1 
1000 
0.976102 
90.179 
1 
0 
2 
2000 
0.00137924 
166.68 
0.001413 
76.502 
3 
3000 
0.00012591 
70.874 
0.000128993 
19.3051 
4 
4000 
1.30793e005 
165.06 
1.33996e005 
74.884 
5 
5000 
9.43717e006 
169.82 
9.66823e006 
79.643 
6 
6000 
1.94354e005 
18.669 
1.99112e005 
108.848 
7 
7000 
2.24247e006 
24.946 
2.29737e006 
115.125 
8 
8000 
1.97063e006 
102.57 
2.01887e006 
192.749 
9 
9000 
5.60066e006 
50.817 
5.73778e006 
39.3625 
This circuit may require more adjustment than it is worth. The
other two are easier to setup and adjust, even in SPICE.
SPICE Model for
circuit of
figure 4^{2}.
Figure 5: Simplest currentfeedback opamp buffer. 

Design Procedure
The design is the same as the first circuit of
figure 3 except for a few changes:
Choose power supplies as
+15V.
Z
_{OUT} = R
_{L} =
1kΩ.
LSK170A has min I
_{DSS} of 2.6mA, choose i
_{D} = 2mA
and calculate
R
_{BE}.
i
_{BQ3} = ((V
_{SS}/Z
_{OUT})  i
_{D})/h
_{fe}
= (15/1kΩ  2mA)/100 = 130µA.
R
_{BE} = v
_{be}/(i
_{D}  i
_{BQ3})
= 700mV/(2mA  130µA) = 374.3315508Ω.
Round up to nearest standard 5% value: R
_{BE} =
390Ω.
r
_{bQ3} = V
_{T}/i
_{BQ3} = 25mV/130µA =
192.3076923Ω. (V
_{T} is the temperature dependent
characteristic voltage of a PN junction, usually 2526mV)
R
_{POLE} = R
_{BE}  r
_{bQ3} = 390Ω 
192.3076923Ω = 128.7978864Ω
C_{POLE} =

1
2πf_{POLE}R_{POLE} 
=

1
2π x 20kHz x 128.7978864Ω 
= 61.78476509nF

C
_{b} = C
_{ibo} + C
_{obo}(A+1) = 10pF +
4.5pF(1kΩ/192.3076923Ω + 1) = 37.9pF (These from 2N3906 datasheet,
multiplying C
_{obo} by A+1 is the Miller effect)
C
_{C} = C
_{POLE}  C
_{b}, because C
_{POLE}
>> C
_{b, }C
_{C} (approx.)= C
_{POLE} =
61.78476509nF.
Choose standard value C
_{C} =
68nF.
R
_{SMAX} = (V
_{p0MAX})/i
_{D} =
(2V)/(700mV/390Ω + 130µA) = 1.039030238kΩ.
Choose R
_{S} =
1.5kΩ
potentiometer (Perhaps it is close enough to try 1kΩ).
SPICE results: 1dB @ 1MHz, 3dB @ 68.6MHz, SNR = 131.9213464dB
Fourier analysis for v(vout) @1V peak:
No. Harmonics: 10, THD: 0.00345022 %, Gridsize: 200,
Interpolation Degree: 1
Harmonic 
Frequency 
Magnitude 
Phase 
Norm. Mag 
Norm. Phase 
 
 
 
 
 
 
0 
0 
0 
0 
0 
0 
1 
1000 
0.997805 
90.009 
1 
0 
2 
2000 
3.83964e006 
117.93 
3.84809e006 
27.921 
3 
3000 
4.24798e006 
10.7399 
4.25733e006 
100.749 
4 
4000 
2.49325e005 
162.05 
2.49874e005 
72.043 
5 
5000 
9.3969e006 
163.01 
9.41758e006 
72.998 
6 
6000 
1.99808e005 
18.7056 
2.00247e005 
108.715 
7 
7000 
2.29573e006 
29.9847 
2.30078e006 
119.994 
8 
8000 
2.14031e006 
103.064 
2.14502e006 
193.073 
9 
9000 
5.77758e006 
50.415 
5.79029e006 
39.5944 
SPICE Model for
circuit of
figure 5^{2}.
Possibly Musical IC Operational Amplifiers^{3}
Amplifiers with dominant pole >= 10kHz created by wide bandwidth and
somewhat lowish open loop gain. Others have claimed excellent
sound from them. Their wide bandwidth will require physically
short feedback paths.
 National Semiconductor: LM6171 (single) and LM6172 (dual).
 Analog Devices: AD826 (dual).
These also have a dominant pole >= 10kHz but I am unaware of any
established reputation.
 Analog Devices: AD817
(single), AD825 (single), and AD847 (single).
 Texas Instruments/Burr Brown: OPA690 (single, OPA2690 dual, OPA3690
triple), OPA820 (single, OPA4820 quad), OPA830 (single, OPA2830 dual, OPA4830
quad), OPA2889 (dual), OPA890 (single, OPA2890 dual)
This decompensated amplifier holds promise of a desireable dominant
pole.
Others
Some Class AB power amplifiers designed and published by G. Randy Slone
have a dominant pole >= 10kHz and were popular while he was selling
kits. This objectivist's use of emitter resistors for local
feedback in the differential front end is another subjectivist friendly
audiophile feature. See his texts to determine which ones.
^{4}
^{1}The Spice
Home Page, visit this link learn about using the SPICE simulator
^{2}Links to supporting SPICE models on this
website: LSK170.txt,
models1.txt
^{3}This listing is not intended to be an
endorsement of the products nor is likely complete. Other ICs may
have similar qualities.
^{4}G. Randy Slone, The Audiophile's Project Sourcebook
(New York, 2002), I made this
discovery while looking at his book shortly before this addition.
Document history
April 29, 2010
Created and immediately updated with lower drain bias for examples.
April 30, 2010 Corrected design procedure of circuit of figure 4.
April 30, 2010 Added minor updates.
May 1, 2010 Corrected all design procedures of circuits of
figures 35 for faulty bias presumptions and updated SPICE models to
match. Original circuits did simulate in SPICE well.
July 19, 2010 Added SPICE distortion profiles for examples at
1kHz and
a leading comment about them, and a list of Possibly Musical IC
Operational Amplifiers.
September 2, 2010 Added to list of Possibly
Musical IC
Operational Amplifiers and added mention of class AB power amplifiers
meeting this article's criteria.
September 18, 2010 Added link to LM6171
datasheet.
September 21, 2010 Deleted AD823 from list of
opamps because it
did not match the scope of this article.
November 2, 2010 Added AD847 to list of Possibly
Musical IC
Operational Amplifiers and a link to its datasheet.