Harmonic Distortion versus Frequency in Amplifiers

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Harmonic Distortion versus Frequency in
Amplifiers
By Jorge Vega Characterization Engineer Raj
Ramanathan Design Engineer Precision Analog
Linear products Op Amps
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Agenda

• Introductory comments
• Measurement setup and THDN
• Tool Blocks
• RMS calculation of THDN
• THDN versus Frequency
• Noise Dominated Region
• THD Dominated Region
• Slew Rate Induced Distortion
• Summary

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Introductory Comments

• What is harmonic distortion and why do we care?

? non-linearity
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Introductory Comments

• What is harmonic distortion and why do we care?
• ? non-linearity

• Types of distortion

• Understanding how noise, input source
  resistance, open loop gain, closed loop gain,
  slew rate, loading all affect distortion

• OPA1652, OPA1662 and OPA1602 ? line of Sound
  Plus Audio Amplifiers. Very low distortion and
  noise amplifiers

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Measurement Tool and THDN?Tool Blocks
Tool of choice in industry Audio Precision 27k
General tool blocks

1. Pure Sine wave generator
2. Fundamental Notch Filter
3. Band Limiting filter
4. RMS detector
5. AC Voltmeter
6. DSP Processing

? Clean signal generator -115dB distortion
0.0001
? Leaves only harmonics. Eliminates fundamental
? Filter settings 22kHz, 30 kHz, 80 kHz 500 kHz
? Converts varying AC signals into rms equivalent
? Measurement of rms values
? FFT is generated
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Measurement Tool and THDN?Tool Blocks ?
Notched Fundamental illustration
Harmonics
Fundamental at 10 kHz
Fundamental removed by notch filter
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Measurement Tool and THDN?RMS calculation of
THDN
Key takeaway Noise dominated region and THD
dominated region
V1 ? Fundamental of the input signal VN ?
Harmonics VNOISE ? Amplifiers noise

• Graphical representation of RMS equation
• Shows THDN measured with different fundamental
  frequencies applied
• 100 Hz fundamental applied ? THDN 0.00001
• 10 kHz fundamental applied ? THDN 0.0001

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Measurement Tool and THDN?RMS calculation of
THDN
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THDN versus Frequency? Noise Dominated Region
OPA1652

• What is a typical configuration?
• Buffer configuration
• Measurement bandwidth set to 80kHz but 500kHz
  equally typical
• Fixed 3Vrms amplitude sinusoid applied while
  sweeping frequency.

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THDN versus Frequency? Noise Dominated Region
OPA1652

• Why is the Noise-dominated region typically
  lowest in THDN values?
• Spectral content dominated by the amplifiers
  noise as opposed to its harmonics.
• Without noise, the curve would continue to
  decrease with a slope of 20 dB/decade at low
  frequencies

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THDN versus Frequency? Noise Dominated Region
OPA1652
Example 1 illustrates the relationship between
noise and distortion. ?The objective will be
to learn how to go back and forth from noise to
THDN and vice versa.
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• THDN versus FrequencyNoise Dominated Region
  ?Example 1

Add value to graph
Keyword
OPA1652
? we get Vrms

• Operation is the same as taking the area under
  the noise density curve.
• It is an approximation since it does not account
  for the flicker noise region.

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• THDN versus FrequencyNoise Dominated Region
  ?Example 1

• Now that we have Vrms how do we get to THDN?

• VN is zero because the harmonics are below the
  noise floor. So we end up with

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• THDN versus FrequencyNoise Dominated Region
  ?Example 1

Example 1
and BW 80kHz , then
where
where VNOISE1.27 uVRMS and V1 3 VRMS then,
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• THDN versus FrequencyNoise Dominated Region
  ?Source Resistance effect on Noise

THDN is affected by the source resistance
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• THDN versus FrequencyNoise Dominated Region
  ?Source Resistance effect on Noise

Gain is 1V/V
Voltage noise intrinsic to the amplifier
Current noise intrinsic to amplifier multiplied
the source resistance
Thermal noise of resistance
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• THDN versus FrequencyNoise Dominated Region
  ?Source Resistance effect on Noise

delta is
Bipolar amplifier
Constant Dominant at Low R
Dominates at High Rsource
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• THDN versus FrequencyNoise Dominated Region
  ?Source Resistance effect on Noise

• Quick questions
• If noise is the only care about
• What amplifier would you want to use if source
  resistance is less than 1kO?
• What if the source resistance is 6kO?
• What effect does this have on THDN?

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• THDN versus FrequencyNoise Dominated Region
  ?Source Resistance effect on THDN

• Higher source resistance yields higher THDN
  because of noise contribution
• Finding THDN from noise is similar to example 1

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• THDN versus FrequencyNoise Dominated Region
  ?Source Resistance effect on THDN
  ?Example 2

where
K 1.38 E-23 J/K
T300K and RS1kO, then
Total integrated noise is obtained as in Example
1.
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• THDN versus FrequencyTHD Dominated Region
  ?Aol and Distortion

• At high frequencies the amplifier becomes more
  non-linear and THDN increases at 20dB per
  decade.
• Region is dominated by THD and not noise.
• Type of distortion is referred to as gain
  roll-off induced distortion

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• THDN versus FrequencyTHD Dominated Region
  ?Example 3 Find THD

• How can we find THD at 10kHz?

• Obtain a Fourier spectrum with 3 Vrms input
  signal set at 10kHz.

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• THDN versus FrequencyTHD Dominated Region
  ?Example 3 Find THD

• Shows which harmonics are dominating
• Shows if THDN is noise or THD dominated
• Used to validates THDN results

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• THDN versus FrequencyTHD Dominated Region
  ?Example 3 Find THD

where V1 0 dB, V2 120.07 dB, V3 124.06
dB, and V4 135.26 dB.
Amplitudes need to be converted to rms power
values.
Thus we have

• Shows that at 10kHz, measurement is THD
• dominated.
• What happens if add noise?

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• THDN versus FrequencyTHD Dominated Region
  ?Example 3 Find THDN

The noise magnitude is VNOISE 0.42 uVrms, then
THDN is
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• THDN versus FrequencyTHD Dominated Region
  ?Aol and Distortion

Open loop gain
Closed loop gain
Loop gain
Feedback factor
What happens to THD if we tweak Aol knob while
leaving the feedback factor fixed at 1?
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• THDN versus FrequencyTHD Dominated Region
  ?Aol and Distortion

Pole
where

• Large open-loop gain yields better correction by
  virtue of negative feedback than when open-loop
  gain is small.

• Open-loop gain decreases with frequency at 20
  dB per decade, the ability of negative feedback
  to correct for the amplifiers inherent
  nonlinearities is degraded with increasing
  frequency.

• THD increases with frequency because the
  amplifier has less open loop gain to correct for
  errors at the input

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THDN versus Frequency? RR Output Stage
?Load Induced Distortion
R-to-R Output Stage

• Open loop gain decreases with loading.
• Output transistor may be trioding with heavy
  loads, at this point all linear bets are off.
• Loss of Aol yields degradation of linearity

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• THDN versus FrequencyTHD Dominated Region
  ?Aol and Distortion

Key Takeaway ? Higher Aol at frequencies of
interest is better for correcting non-linearities
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• THDN versus FrequencyTHD Dominated Region
  ?Aol and Distortion

Open loop gain
Closed loop gain
Loop gain
Feedback factor
What happens to THDN if we tweak Beta knob while
leaving the Aol fixed at 120dB?
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• THDN versus FrequencyTHD Dominated Region
  ?Closed Loop Gain and Distortion

• Lower closed loop gain yields higher Loop Gain
• Good for distortion

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• THDN versus FrequencyTHD Dominated Region
  ?Closed Loop Gain and Distortion

• Distortion is 10x worse in a gain of 10V/V
  compared to gain 1V/V
• THD worsens with closed loop gain because the
  amplifier has less loop gain to correct for
  errors at the input

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THDN versus Frequency?Slew Rate Induced
Distortion

• What happens if we keep going up in frequency?

• Distortion grossly increases and reaches
  Slew-rate induced distortion

• To see this we need to understand the
  relationship between fullpower bandwidth and slew
  rate.

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THDN versus Frequency?Slew Rate Induced
Distortion ? Full Power Bandwidth and Slew Rate
If the output signal is given by
375kHz
after deviating we have
where
The maximum slew rate occurs when the cosine term
is 1. Thus, we have
If SR 10V/us and Vp 4.24Vp then the max
frequency is 375kHz
So if the amplifier is fed a 3Vrms (same as
4.24Vp) signal, at a frequency of 375kHz the
amplifier will be slew rate limited
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THDN versus Frequency?Slew Rate Induced
Distortion

• The amplifiers negative feedback is not fast
  enough to keep up with the input.
• Output cannot swing completely and gross
  degradation of linearity occurs.

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• THDN versus FrequencyPratical tips

Practical Tips for low THDN in your application
design
1. Minimize the resistor value connected to the
positive and negative inputs , it increases noise.
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• THDN versus FrequencyPratical tips

Practical Tips for low THDN in your application
design
1. Minimize the resistor value connected to the
positive and negative inputs , it increases noise.
2. Select amplifier with low THD, high Aol at
frequencies of operation, and high slew rate.
3. Minimize gains. Lower closed-loop gain means
higher loop gain
4. Reduce loading as much as possible on the
amplifier, it hurts Aol.
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• THDN versus FrequencyPratical tips

Practical Tips for low THDN in your application
design
1. Minimize the resistor value connected to the
positive and negative inputs , it increases noise.
2. Select amplifier with low THD, high Aol at
frequencies of operation, and high slew rate.
3. Minimize gains. Lower closed-loop gain means
higher loop gain
4. Reduce loading as much as possible on the
amplifier, it hurts Aol.

• 5. Use power-supply bypass capacitors
• Bulk caps 4.7uF to 10uF within 1 inch of power
  pins.
• High frequency caps 10nF to 100nF within 0.1 inch
  of power pins.
• Use mica if possible for high frequency.

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• THDN versus FrequencyPratical tips

Practical Tips for low THDN in your application
design
1. Minimize the resistor value connected to the
positive and negative inputs , it increases noise.
2. Select amplifier with low THD, high Aol at
frequencies of operation, and high slew rate.
3. Minimize gains. Lower closed-loop gain means
higher loop gain
4. Reduce loading as much as possible on the
amplifier, it hurts Aol.

• 5. Use power-supply bypass capacitors
• Bulk caps 4.7uF to 10uF within 1 inch of power
  pins.
• High frequency caps 10nF to 100nF within 0.1 inch
  of power pins.
• Use mica if possible for high frequency.

6. Remove ground planes underneath amplifier and
use minimum feedback resistor values so as to
avoid effects of parasitic capacitance.
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Summary

• Types of distortion
• Noise dominated distortion
• Gain roll-off induced distortion
• Slew induced distortion
• Practical tips

• Things to look forward to
• THDN versus Amplitude plots and their
  significance
• Measuring lower than -120dB (the Audio
  Precisions noise floor)
• Troubleshooting THDN values with reading
  channel
• 4. Effects of temperature on distortion Thermal
  Distortion

• Acknowledgements
• Art Kay, Bruce Trump, Randy Heilman
• References
• Bob Metzlers Audio Precision Measurement
  Handbook
• James Karkis Designing for low distortion with
  high speed opamps
• Gray and Meyer

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THDN versus Frequency
Back up slides
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• THDN versus FrequencyTHD Dominated Region
  ?Closed Loop Gain and Distortion

• The closed loop equation for an op amp is given
  by

• The larger the open loop gain, the more ACL
  resembles 1/ß.
• The noise gain in an op amp, NG, is given by
  1/ß, so the equation can be rewritten as

, then

• The ratio of NG/AOL is an error term.
• As the noise gain increases, the error term
  increases. The effect is that the amplifier
  distortion worsens because it has less loop gain
  to linearize the distortion error.