Updated September 2, 2016.  See Document History at end for details.

# One-Bend Amplifier

Part 4: Improvements include lower hum

### Introduction

After the number of output transistors was increased to eight to improve the thermal analysis it was deemed also that an improvement in hum was likely if the inner feedback loop returned to the cascode of the first stage rather than directly to the second.  Therefore I deemed it necessary to implement the changes and re-validate the SPICE analysis.  Circuits and analysis follow.

### Circuits

Note:  Component values can be obtained from the SPICE models for now.

 Figure 1:  Amplifier Schematic
SPICE model

 Figure 2:  Unregulated power supply
SPICE model

 Figure 3:  Regulated power supply
SPICE model

### Spice Results

Begin hum measurements with unregulated supply to first two stages

Fourier analysis for vout:
No. Harmonics: 16, THD: 67.8647 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Decibels 1 120 0.00295888 -50.5775 2 240 0.00144109 -56.8262 3 360 0.000940647 -60.5315 4 480 0.00066636 -63.5258 5 600 0.000506254 -65.9126 6 720 0.000385225 -68.2857 7 840 0.00030367 -70.352 8 960 0.000233349 -72.6399 9 1080 0.000184023 -74.7026 10 1200 0.000138508 -77.1705 11 1320 0.000106726 -79.4346 12 1440 7.62605E-05 -82.354 13 1560 5.59989E-05 -85.0364 14 1680 3.58895E-05 -88.9007 15 1800 2.37921E-05 -92.4713

Calculate total hum from apparent THD.

 (1) vhum = vhum1 ×  (1 + THDapparent) = 0.00295888 × (1 + 0.678647 ) = 4.96692mV

 (2) vhum = 20log(4.96692mV) = -46.0783dBV

Because hum is higher than suspected, go back to supply regulating first two stages and analyze again

Fourier analysis for vout:
No. Harmonics: 16, THD: 74.2546 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Decibels 1 120 9.80761E-07 -120.169 2 240 4.71169E-07 -126.536 3 360 3.25877E-07 -129.739 4 480 2.36987E-07 -132.506 5 600 1.93989E-07 -134.244 6 720 1.59653E-07 -135.936 7 840 1.37583E-07 -137.220 8 960 1.20571E-07 -138.375 9 1080 1.06839E-07 -139.425 10 1200 9.66625E-08 -140.295 11 1320 8.76482E-08 -141.145 12 1440 8.05205E-08 -141.882 13 1560 7.44112E-08 -142.567 14 1680 6.9202E-08 -143.198 15 1800 6.45515E-08 -143.802

Calculate total hum from apparent THD.

 (3) vhum = vhum1 ×  (1 + THDapparent) = 9.80761e-07 × (1 + 0.742546 ) = 1.70902µV

 (4) vhum = 20log(1.70902µV) = -115.345dBV

Now that hum is acceptable continue with distortion analysis at 1kHz.

Fourier analysis for vout:
No. Harmonics: 16, THD: 0.0152017 %, Gridsize: 200, Interpolation Degree: 3

 Harmonic Frequency Magnitude Norm.Mag Percent Decibels 1 1000 21.1954 1 100 0 2 2000 0.00321471 0.00015167 0.015167 -76.382 3 3000 0.000216674 1.02227E-05 0.00102227 -99.8087 4 4000 1.73009E-05 8.16258E-07 8.16258E-05 -121.763 5 5000 1.55152E-06 7.32006E-08 7.32006E-06 -142.71 6 6000 1.34958E-07 6.36731E-09 6.36731E-07 -163.921 7 7000 2.64258E-08 1.24677E-09 1.24677E-07 -178.084 8 8000 3.92902E-08 1.85372E-09 1.85372E-07 -174.639 9 9000 2.10337E-08 9.92371E-10 9.92371E-08 -180.067 10 10000 1.5393E-08 7.26245E-10 7.26245E-08 -182.778 11 11000 1.76767E-08 8.33989E-10 8.33989E-08 -181.577 12 12000 4.92896E-09 2.32549E-10 2.32549E-08 -192.67 13 13000 3.43396E-08 1.62014E-09 1.62014E-07 -175.809 14 14000 2.99262E-08 1.41192E-09 1.41192E-07 -177.004 15 15000 2.39516E-08 1.13004E-09 1.13004E-07 -178.938

Validate the remainder of the design.

 Figure 4:  Stability analysis  showing 85º of  phase margin.

 Figure 5:  Small signal error curve. Shows dominance of second harmonic. Figure 6:  Large signal error curve. Shows dominance of second harmonic then third.

 Figure 7:  Bode shows frequency response down 3dB at 495kHz

### Conclusions

Hum is considerably improved relative to the last implementation with regulation however not enough to be rid of the regulators altogether.  The remainder of the analysis remains as good as before.

1Note:  Raw Fourier analysis data has been processed in spreadsheet to calculate related results and reformatted.
2See related article:  Thermal Design Part 2.
3See related article:  Floating Source-follower Regulator.

Document History
August 20, 2016  Created.
August 27, 2016  Added note to get component values from SPICE models added missing equation numbers for calculations.
September 2, 2016  Minor correction to caption to figure 7.