1. Progress In Power Amplifier Design
AES WARSAW 2015
Engineering Brief EB-2-2
Progress In Power Amplifier Design
Thermal Distortion
Douglas Self

2. Power amplifier imperfections
Frequency response: no problem
Slew-rate: no problem
Noise: Blameless amplifier with differential pair
input has an EIN of approx -123 dBu.
Gain of 23 times: (+27 dB) output noise is -96 dBu.
Add only a 5534 voltage follower in front;
amplifier output noise goes up 3 dB
Distortion: still with us

3. Blameless power amplifier: CFP output stage

4. Power amplifier distortions
CONFIGURATION
D1: Input stage non-linearity
D2: Voltage Amplifier Stage (VAS) non-linearity
D3: Output stage non-linearity
D4: Non-linear loading of VAS
TOPOLOGY
D5: Decoupling ground problems
D6: Rail induction
D7: Negative feedback takeoff point errors
This list assumes the use of the standard Blameless configuration. This classification assumes no clipping, overload, slew-limiting, or parasitic oscillation.
COMPONENTS
D8: Capacitor distortion (NFB cap, compensation cap

5. More power amplifier distortions
INTERFACING
D9: Magnetic conductor distortion (relay frames, terminals)
D10: Non-linear input currents flowing in significant
source impedances
D11: Premature operation of SOAR protection

6. Distortions to not worry about
ND1: Input-Stage Common-Mode Distortion.
Only important at very low closed-loop
gains
ND2: Thermal Distortion over a cycle. Not to
be confused with slow bias changes in
a Class-B output stage. Would cause rise in
THD at LF; not previously observed
But... with better test gear and higher output levels of up to 100W/8Ω, a rise in THD at LF is visible...
A quick digression as to why these distortion mechanisms are not a source of concern.
For example, you often see cascode input stages recommended as a cure for input-stage CM distortion.

7. THD of Compact Class-B CFP power amp: no-load, 20W/16Ω, 40W/8Ω, 80W/4Ω and genmon. Normal Miller compen.
Measurement bwidth kHz

8. 40W/8Ω = dBu
0.0003% = dB
Thus indicated noise floor is at dBu
Amplifier alone has noise floor at -96 dBu
So AP noise limits the measurement here

9. LF THD is essentially not a function of output current
LF THD is essentially not a function of output current. (slightly at 4Ω)
It rises very slowly as frequency falls; takes three octaves to double in amplitude.

10. Also, LF THD:
Increases with output voltage, more steeply as output voltage increases
Is not a function of supply voltage
The feedback capacitor is not involved. Doubling its size made no difference.
Is not affected by the compensation scheme used (eg output inclusive compensation)
Implies source of LF distortion is not in amplifier forward path.

11. Standard NFB network. 332 mW in 750mW resistor Rnfb1
15 mW in resistor Rnfb2

12. The most severe conditions for any passive component in the amplifier.
Thermal distortion?
At 100W/8Ω output, upper feedback resistor Rnfb1 dissipates 332 mW. See resistor temp coefficient.
At 100W/8Ω output, upper feedback resistor Rnfb1 has
27 Vrms (40 Vpeak) across it. See resistor voltage coefficient.
The most severe conditions for any passive component in the amplifier.

13. Distortion models
Straightforward for voltage-coefficent distortion. All odd harmonics are generated, and all have a THD % proportional to signal level; see APAD6.
Much more complicated for thermal distortion as heat spreading out from surface film into resistor body is hard to model. FEA approach required.

14. Four 250 mW resistors in parallel Power reduced to 1/4
Voltage the same
LF distortion reduced by a factor of 0.77 times,
slope vs freq unchanged
Eight 250 mW resistors in parallel
Power reduced to 1/8
Voltage the same
LF distortion reduced by a factor of 0.55 times,
slope vs freq unchanged
Suggests power and not
voltage is the issue.

15. Four resistors in series-parallel
Power reduced to 1/4, voltage halved
Samples: 2k2 750mW ±100 ppm/°C Metal Film
PR 2k2 500mW ±50 ppm/°C Metal Film
Same highly reputable manufacturer

16. THD of Compact Class-B CFP power amp 100W/8Ω
Single k2 750mW ±100 ppm/°C MF resistor BROWN
Single PR 2k2 500mW ±50 ppm/°C MF resistor RED
Test gear output labelled ‘genmon’. Bandwidth kHz

17. THD of Compact Class-B CFP power amp 100W/8Ω
Appears to show we have done all we can with tempco and voltage coeff of top NFB resistor
THD of Compact Class-B CFP power amp 100W/8Ω
Single k2 750mW ±100 ppm/°C MF resistor BROWN
Single PR 2k2 500mW ±50 ppm/°C MF resistor RED
Series-parallel 4x PR 2k2 500mW ±50 ppm/°C MF resistor BLUE
Test gear output labelled ‘genmon’. Bandwidth kHz

18. Added to the distortion list
D12: Thermal distortion in the upper feedback resistor
But LF distortion still visible in previous plot, although thermal distortion from upper resistor now negligible.
Likely to be outside NFB loop- probably thermal effects affecting accuracy of the NFB subtraction by the input pair, so perhaps:
D13: Thermal distortion in input pair ??
Work in progress.
THE END

19. Other resistor types
An old 2% 250 mW MF resistor was tried in an attempt to show some bad thermal distortion. However, despite being run at 30% above its rating, THD was the same as for the PR 500mW ±50 ppm/°C MF resistor.
MORAL: this is an area where you can’t take things for granted. Test!

20. Progress in Power Amplifier Design
AES WARSAW 2015
Engineering Brief EB-2-2
Progress in Power Amplifier Design
Thermal Distortion
douglas-self.com