Transcript THD+N versus Frequency

1
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
1.
Introductory comments
2.
Measurement setup and THD+N
a. Tool Blocks
b. RMS calculation of THD+N
3.
THD+N versus Frequency
a. Noise Dominated Region
b. THD Dominated Region
c.
4.
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 THD+N
Tool Blocks
Tool of choice in industry:
Audio Precision
~ 27k$
General tool blocks:
1.
2.
3.
4.
5.
6.
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Pure Sine wave generator  Clean signal generator ~ -115dB distortion ~ 0.0001%
Fundamental Notch Filter  Leaves only harmonics. Eliminates fundamental
Band Limiting filter  Filter settings 22kHz, 30 kHz, 80 kHz & 500 kHz
RMS detector  Converts varying AC signals into rms equivalent
AC Voltmeter  Measurement of rms values
DSP Processing  FFT is generated
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3
4
5
6
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Measurement Tool and THD+N
Tool Blocks
 Notched Fundamental illustration
Frequency Spectrum (fundamental = 10 kHz)
-20
Notched Fundamental
with Fundamental
Harmonics
-40
Volatage (dB)
Fundamental at 10 kHz
-60
-80
-100
-120
-140
1,000
10,000
Frequency (Hz)
Fundamental removed by notch filter
100,000
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Measurement Tool and THD+N
RMS calculation of THD+N
Recognize RMS operation in THD+N
RMS sum of THD+N
Wideband noise
THD
 V  V

THD  N (%) 
n2
Key takeaway:
Noise dominated region and
THD dominated region
2
N
2
NOISE
2
1
V
100
V1  Fundamental of the input signal
VN  Harmonics
VNOISE  Amplifier’s noise
• Graphical representation of RMS equation
• Shows THD+N measured with different fundamental frequencies applied
• 100 Hz fundamental applied  THD+N = 0.00001%
• 10 kHz fundamental applied  THD+N = 0.0001%
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Measurement Tool and THD+N
RMS calculation of THD+N
Recognize RMS operation in THD+N
RMS sum of THD+N
Wideband noise
THD
Frequency Spectrum (fundamental = 10 kHz)
Frequency Spectrum (fundamental = 100 Hz)
-20
0
Notched Fundamental
Notched Fundamental
with Fundamental
Amplitude (dB)
-40
Amplitude (dB)
with Fundamental
-40
-20
Noise dominated
-60
-80
-60
THD dominated
-80
-100
-100
-120
-120
-140
10
100
1,000
Frequency (Hz)
10,000
100,000
-140
1,000
10,000
Frequency (Hz)
100,000
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THD+N 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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THD+N versus Frequency
 Noise Dominated Region
OPA1652
Why is the Noise-dominated region typically lowest in THD+N values?
 Spectral content dominated by the amplifier’s 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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THD+N 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 THD+N and vice versa.
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THD+N versus Frequency
Noise Dominated Region
Example 1
Add value to graph
OPA1652 Noise from datasheet
Keyword
OPA1652
• If we know the noise density in
VRMS
Hz
, what happens if we multiply by:
Hz ?  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.
THD+N versus Frequency
Noise Dominated Region
Example 1
• Now that we have Vrms how do we get to THD+N?
 V  V

THD  N (%) 
n2
2
N
2
1
V
2
NOISE
100
• VN is zero because the harmonics are below the noise floor. So we end up with:
2
VNOISE
VNOISE
THD  N (%) 

100

100
2
V1
V1
• V1 is the fundamental
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THD+N versus Frequency
Noise Dominated Region
Example 1
Example 1
VNOISE  EO * BW
VNOISE  4.5
nVRMS
Hz
where
EO  4.5
nVRMS
Hz
and BW = 80kHz , then
* 80kHz  1.27uVRMS
VNOISE
where VNOISE=1.27 uVRMS and V1 = 3 VRMS then,
V1
1.27uVRMS
N% 
* 100  0.000042%
3VRMS
N
OPA1652
Matches!
~0.00004%
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THD+N versus Frequency
Noise Dominated Region
Source Resistance effect on Noise
THD+N is affected by the source resistance:
-
-
+
+
RSource
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THD+N versus Frequency
Noise Dominated Region
Source Resistance effect on Noise
Gain is 1V/V
E  e  iN  RS   4KTRS
2
O
2
N
2
Voltage noise intrinsic to the
amplifier
Current noise intrinsic to
amplifier multiplied the
source resistance
Thermal noise of resistance
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THD+N versus Frequency
Noise Dominated Region
Source Resistance effect on Noise
Voltage Noise versus Source Resistance
OPA1662: Bipolar Amplifier
1000
OPA1652: CMOS Amplifier
Volatge Noise (Vrms/rtHz)
Resistor Thermal Noise
Bipolar Amp Noise + Thermal Resistor Noise
100
CMOS amplifier
Dominates at
High Rsource
E  e  4 KTRS
2
O
2
N
delta is iN  RS
10
1
100
Constant &
Dominant at
Low R
CMOS Amp Noise + Thermal Resistor Noise
1,000
10,000
Resistance (Ω)
100,000
Bipolar amplifier
Constant &
Dominant at
Low R
Dominates at
High Rsource
EO2  eN2  iN  RS   4KTRS
2
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THD+N versus Frequency
Noise Dominated Region
Source Resistance effect on Noise
Voltage Noise versus Source Resistance
OPA1662: Bipolar Amplifier
1000
OPA1652: CMOS Amplifier
Volatge Noise (Vrms/rtHz)
Resistor Thermal Noise
Bipolar Amp Noise + Thermal Resistor Noise
100
CMOS Amp Noise + Thermal Resistor Noise
10
1
100
1,000
10,000
Resistance (Ω)
100,000
Quick questions:
If noise is the only care about:
• What amplifier would you want to use if source resistance is less than 1kΩ?
• What if the source resistance is ~ 6kΩ?
• What effect does this have on THD+N?
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THD+N versus Frequency
Noise Dominated Region
Source Resistance effect on THD+N
Open
Bipolar Amplifier
• Higher source resistance yields higher THD+N because of noise contribution
• Finding THD+N from noise is similar to example 1
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THD+N versus Frequency
Noise Dominated Region
Source Resistance effect on THD+N
Example 2
EO2  eN2  iN  RS   4KTRS
nVRMS
eN  2.5
iN  1.8
Hz
2
2
where
pA
Hz
K = 1.38 E-23 J/K
T=300K and RS=1kΩ, then
2
nV  
nV
pA
J

 

EO   2.5 RMS   1.8
1k    4 1.38E  23  300 K 1k   5.1 RMS
K
Hz  
Hz
Hz


 
Total integrated noise is obtained as in Example 1.
Open
nV
VNOISE  5.1 RMS * 80kHz  1.44uVRMS
Hz
V
1.44uVRMS
N  NOISE % 
*100%  0.000048%
V1
3VRMS
0.00005%
THD+N versus Frequency
THD Dominated Region
Aol and Distortion
• At high frequencies the amplifier becomes more non-linear and THD+N 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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THD+N versus Frequency
THD 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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THD+N versus Frequency
THD Dominated Region
Example 3 : Find THD
• Shows which harmonics are dominating
• Shows if THD+N is noise or THD dominated
• Used to validates THD+N results
 V  V

THD  N (%) 
n2
2
N
V12
2
NOISE
100
THD+N versus Frequency
THD Dominated Region
Example 3: Find THD

THD (%) 
4
n2
2
1
V
VN2
V22  V32  V42
 100 
 100
V12
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.
V1  10
0 dB
20 dB
V2  10
V3  10
V4  10
 1,
120.07 dB
20 dB
124.06 dB
20 dB
135.26 dB
20 dB
 9.921E  07Vrms,
 6.267 E  07Vrms,
 1.725 E  07Vrms
Thus we have:
THD (%) 
(9.921E  07) 2  (6.267 E  07) 2  (1.725 E  07) 2
100
12
THD (%)  0.000118%
• Shows that at 10kHz, measurement is THD
dominated.
• What happens if add noise?
0.000126%
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THD+N versus Frequency
THD Dominated Region
Example 3: Find THD+N
The noise magnitude is VNOISE = 0.42 uVrms, then THD+N is:
 V   V
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THD  N (%) 
THD  N (%) 
n2
2
N
2
1
2
Noise
V
2
V22  V32  V42  VNoise
 100 
 100
V12
(9.921E  07) 2  (6.267 E  07) 2  (1.725 E  07) 2  (0.42 E  06) 2
100
12
THD  N (%)  0.000126%
Matches!
0.000126%
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THD+N versus Frequency
THD Dominated Region
Aol and Distortion
Open loop gain
AOL
ACL 
1  AOL 
Closed loop gain
Loop gain
Equation has two knobs:
1. .AOL
2. Feedback factor

Feedback
factor
What happens to THD if we
tweak Aol knob while leaving the
feedback factor fixed at 1?
AOL
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THD+N versus Frequency
THD Dominated Region
Aol and Distortion
ACL 
Pole
THD+N & Open Loop Gain versus Frequency
THD+N
THD
THD
OpenOpen
Loop Loop
Gain Gain
0.01
160
140
AOL slope = -20dB/dec
100
0.0001
noise dominated
80
60
0.00001
40
ACL 
20
THD slope = +20dB/dec
0.000001
where
0
0.0000001
1
10
100
1,000
 1
120
Open Loop Gain (dB)
0.001
THD+N (%)
AOL
1  AOL 
10,000
100,000
1,000,000
10,000,000
-20
100,000,000
Frequency (Hz)
• 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 amplifier’s 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
AOL
1  AOL
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THD+N versus Frequency
R-to-R Output Stage
 RR Output Stage
Load Induced Distortion
+Vs
+Vs
RLOAD
-Vs
• 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
RLOAD
-Vs
THD+N versus Frequency
THD Dominated Region
Aol and Distortion
Key Takeaway  Higher Aol at frequencies of interest is better for
correcting non-linearities
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THD+N versus Frequency
THD Dominated Region
Aol and Distortion
Open loop gain
AOL
ACL 
1  AOL 
Closed loop gain
Loop gain
Equation has two knobs:
1. .AOL
2. Feedback factor

Feedback
factor
What happens to THD+N if we
tweak Beta knob while leaving
the Aol fixed at 120dB?

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THD+N versus Frequency
THD Dominated Region
Closed Loop Gain and Distortion
Gain versus Frequency
Gain versus Frequency
Open Loop Gain
Closed Loop Gain = 1
100
100
80
80
60
60
40
Gain (dB)
Gain (dB)
Open Loop Gain
Larger Loop Gain
40
20
20
0
0
-20
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
-20
1,000
Closed Loop Gain = 10
Smaller Loop Gain
10,000
Frequency (Hz)
• Lower closed loop gain yields higher Loop Gain
• Good for distortion
100,000
1,000,000
Frequency (Hz)
10,000,000
100,000,000
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THD+N versus Frequency
THD Dominated Region
Closed Loop Gain and Distortion
THD+N versus Frequency
Closed Loop Gain = 1
Closed Loop Gain = 10
0.01
THD+N (%)
0.001
0.0001
0.00001
10
100
1,000
Frequency (Hz)
10,000
100,000
• 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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THD+N 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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THD+N versus Frequency
Slew Rate Induced Distortion
 Full Power Bandwidth and Slew Rate
If the output signal is given by:
Vout  VpSin(  t )
Then slew rate is:
375kHz
dV
d
SR  out  VpSin (  t )
dt
dt
after deviating we have:
SR   VpCos(  t )
where
  2  f
The maximum slew rate occurs when the cosine term is 1. Thus, we have:
SR  2  f Vp
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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THD+N versus Frequency
Slew Rate Induced Distortion
• The amplifier’s 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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THD+N versus Frequency
Pratical tips
Practical Tips for low THD+N in your application design
1. Minimize the resistor value connected to the positive and negative inputs , it increases noise.
R1
RF
-
+
+
RS
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THD+N versus Frequency
Pratical tips
Practical Tips for low THD+N 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.
R1
RF
+Vs
-
+Vs
RLOAD
RLOAD
+
+
RS
RLoad
-Vs
-Vs
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THD+N versus Frequency
Pratical tips
Practical Tips for low THD+N 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.
dI
V L
dt
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THD+N versus Frequency
Pratical tips
Practical Tips for low THD+N 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:
1. Noise dominated distortion
2. Gain roll-off induced distortion
3. Slew induced distortion
4. Practical tips
Things to look forward to:
1. THD+N versus Amplitude plots and their significance
2. Measuring lower than -120dB (the Audio Precision’s noise floor)
3. Troubleshooting THD+N values with “reading channel”
4. Effects of temperature on distortion: Thermal Distortion
Acknowledgements:
Art Kay, Bruce Trump, Randy Heilman
References:
• Bob Metzler’s Audio Precision Measurement Handbook
• James Karki’s Designing for low distortion with high speed opamps
• Gray and Meyer
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THD+N versus Frequency
Back up slides
THD+N versus Frequency
THD Dominated Region
Closed Loop Gain and Distortion
• The closed loop equation for an op amp is given by:
ACL 
AOL
1  AOL 
• The larger the open loop gain, the more ACL resembles 1/β.
• The noise gain in an op amp, NG, is given by 1/β, so the equation can be rewritten as::
ACL 
AOL
N G AOL

A
AOL  N G
1  OL
NG
, then
ACL 
NG
N 
1   G 
 AOL 
• 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.
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