Harmonic Distortion versus Frequency in Amplifiers

1

Harmonic Distortion versus Frequency in Amplifiers

By Jorge Vega – Characterization Engineer&

Raj Ramanathan – Design Engineer

Precision Analog – Linear products – Op Amps

2

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. Slew Rate Induced Distortion

4. Summary

Agenda

3

Introductory Comments

• What is harmonic distortion and why do we care?

non-linearity

4

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

5

Measurement Tool and THD+NTool Blocks

Tool of choice in industry: Audio Precision~ 27k$

General tool blocks:1. Pure Sine wave generator 2. Fundamental Notch Filter3. Band Limiting filter 4. RMS detector5. 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

1 2 3 4 5 6

6

Frequency Spectrum (fundamental = 10 kHz)

-140

-120

-100

-80

-60

-40

-20

1,000 10,000 100,000

Frequency (Hz)

Vol

atag

e (d

B)

Notched Fundamental with Fundamental

Measurement Tool and THD+NTool Blocks Notched Fundamental illustration

Fundamental removed by notch filter

Fundamental at 10 kHz

Harmonics

7

Measurement Tool and THD+NRMS calculation of THD+N

100(%)

21

2

22

V

VVNTHD n NOISEN

V1 Fundamental of the input signalVN 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%

THD Wideband noise

RMS sum of THD+N

Recognize RMS operation in THD+N Key takeaway:Noise dominated region and THD dominated region

8

Measurement Tool and THD+NRMS calculation of THD+N

THD Wideband noise

RMS sum of THD+N

Recognize RMS operation in THD+N

Frequency Spectrum (fundamental = 100 Hz)

-140

-120

-100

-80

-60

-40

-20

0

10 100 1,000 10,000 100,000

Frequency (Hz)

Am

plitu

de (

dB)


Noise dominated

Frequency Spectrum (fundamental = 10 kHz)

-140

-120

-100

-80

-60

-40

-20

1,000 10,000 100,000

Frequency (Hz)

Am

plitu

de (

dB

)


THD dominated

9

THD+N versus Frequency Noise Dominated Region

What is a typical configuration?

• Buffer configuration

• Measurement bandwidth set to 80kHz but 500kHz equally typical

• Fixed 3Vrms amplitude sinusoid applied while sweeping frequency.

OPA1652

10


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

OPA1652

11


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.

OPA1652

12

OPA1652 Noise from datasheet

THD+N versus FrequencyNoise Dominated Region Example 1

• 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.

Keyword

• If we know the noise density inHz

VRMS , what happens if we multiply by: Hz ? we get Vrms

Add value to graph

OPA1652

13THD+N versus FrequencyNoise Dominated Region Example 1

• Now that we have Vrms how do we get to THD+N?

100(%)

21

2

22

V

VVNTHD n NOISEN

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

100100(%)1

21

2

V

V

V

VNTHD NOISENOISE

• V1 is the fundamental

14THD+N versus FrequencyNoise Dominated Region Example 1

BWEV ONOISE *Hz

nVE RMS

O 5.4

RMSRMS

NOISE uVkHzHz

nVV 27.180*5.4

Example 1

where and BW = 80kHz , then

1V

VN NOISE

%000042.0100*3

27.1%

RMS

RMS

V

uVN

where VNOISE=1.27 uVRMS and V1 = 3 VRMS then,

~0.00004%

Matches!

OPA1652

15THD+N versus FrequencyNoise Dominated Region Source Resistance effect on Noise

-

+

RSource

-

+

THD+N is affected by the source resistance:


SSNNO KTRRieE 4222

Voltage noise intrinsic to the amplifier

Current noise intrinsic to amplifier multiplied the source resistance

Thermal noise of resistance

Gain is 1V/V


Dominates at High Rsource

SSNNO KTRRieE 4222

Bipolar amplifier

Constant &Dominant at Low R

Dominates at High Rsource

CMOS amplifier

SNO KTReE 422

Constant &Dominant at Low R

delta is SN Ri

Voltage Noise versus Source Resistance

1

10

100

1000

100 1,000 10,000 100,000Resistance (Ω)

Vo

latg

e N

oise

(V

rms/

rtH

z)

Resistor Thermal Noise

Bipolar Amp Noise + Thermal Resistor Noise

CMOS Amp Noise + Thermal Resistor Noise

OPA1652: CMOS Amplifier

OPA1662: Bipolar Amplifier

18

Voltage Noise versus Source Resistance

1

10

100

1000

100 1,000 10,000 100,000Resistance (Ω)

Vo

latg

e N

oise

(V

rms/

rtH

z)

Resistor Thermal Noise

Bipolar Amp Noise + Thermal Resistor Noise

CMOS Amp Noise + Thermal Resistor Noise

THD+N 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 1kΩ?• What if the source resistance is ~ 6kΩ?• What effect does this have on THD+N?

OPA1652: CMOS Amplifier

OPA1662: Bipolar Amplifier

19THD+N versus FrequencyNoise Dominated Region Source Resistance effect on THD+N

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

Bipolar Amplifier

Open

20THD+N versus FrequencyNoise Dominated Region Source Resistance effect on THD+N Example 2

SSNNO KTRRieE 4222

Hz

nVe RMS

N 5.2Hz

pAiN 8.1

Hz

nVkK

K

JEk

Hz

pA

Hz

nVE RMSRMS

O 1.513002338.1418.15.222

%000048.0%100*3

44.1%

44.180*1.5

1

RMS

RMSNOISE

RMSRMS

NOISE

V

uV

V

VN

uVkHzHz

nVV

where

K = 1.38 E-23 J/K T=300K and RS=1kΩ, then

Total integrated noise is obtained as in Example 1.

0.00005%

Open

21THD+N versus FrequencyTHD 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”

22THD+N 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.

23THD+N versus FrequencyTHD Dominated Region Example 3 : Find THD

100(%)

21

2

22

V

VVNTHD n NOISEN

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

24THD+N versus FrequencyTHD Dominated Region Example 3: Find THD

100100(%)21

24

23

22

21

4

2

2

V

VVV

V

VTHD n N

VrmsEV

VrmsEV

VrmsEV

V

dB

dB

dB

dB

dB

dB

dB

dB

07725.110

,07267.610

,07921.910

,110

20

26.135

4

20

06.124

3

20

07.120

2

20

0

1

%000118.0(%)

1001

)07725.1()07267.6()07921.9((%) 2

222

THD

EEETHD

where: V1 = 0 dB, V2 = –120.07 dB, V3 = –124.06 dB, and

V4 = –135.26 dB.

Thus we have:

Amplitudes need to be converted to rms power values.

• Shows that at 10kHz, measurement is THD

dominated.

• What happens if add noise?

0.000126%

25

100100(%)

21

224

23

22

21

4

2

22

V

VVVV

V

VVNTHD Noisen N Noise

%000126.0(%)

1001

)0642.0()07725.1()07267.6()07921.9((%)

2

2222

NTHD

EEEENTHD

The noise magnitude is VNOISE = 0.42 uVrms, then THD+N is:

THD+N versus FrequencyTHD Dominated Region Example 3: Find THD+N

0.000126%

Matches!


OL

OLCL A

AA

1

Closed loop gain

Loop gain

Open loop gain

Equation has two knobs:

1. .

2. Feedback factor OLA

Feedback factor

What happens to THD if we tweak Aol knob while leaving the feedback factor fixed at 1?

OLA

27

THD+N & Open Loop Gain versus Frequency

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000

Frequency (Hz)

TH

D+

N (

%)

-20

0

20

40

60

80

100

120

140

160

Ope

n Lo

op G

ain

(dB

)

THD Open Loop Gain

THD slope = +20dB/dec

AOL slope = -20dB/dec

THD+N versus FrequencyTHD Dominated Region Aol and Distortion

OL

OLCL A

AA

1

• 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

1

OL

OLCL A

AA

1

where

THD+N & Open Loop Gain versus Frequency

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000

Frequency (Hz)

TH

D+

N (

%)

-20

0

20

40

60

80

100

120

140

160

Ope

n Lo

op G

ain

(dB

)

THD+N THD Open Loop Gain

THD slope = +20dB/dec

AOL slope = -20dB/dec

noise dominated

Pole

28

R-to-R Output Stage+V s

R LO AD R LO AD

+V s

-Vs-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

THD+N versus Frequency RR Output Stage

Load Induced Distortion


Key Takeaway Higher Aol at frequencies of interest is better for correcting non-linearities


OL

OLCL A

AA

1

Closed loop gain

Loop gain

Open loop gain

Equation has two knobs:

1. .

2. Feedback factor OLA

Feedback factor

What happens to THD+N if we tweak Beta knob while leaving the Aol fixed at 120dB?

31THD+N versus FrequencyTHD Dominated Region Closed Loop Gain and Distortion

Gain versus Frequency

-20

0

20

40

60

80

100

1,000 10,000 100,000 1,000,000 10,000,000 100,000,000

Frequency (Hz)

Gai

n (d

B)

Open Loop Gain Closed Loop Gain = 1

Larger Loop Gain

Gain versus Frequency

-20

0

20

40

60

80

100

1,000 10,000 100,000 1,000,000 10,000,000 100,000,000

Frequency (Hz)

Gai

n (d

B)

Open Loop Gain Closed Loop Gain = 10

Smaller Loop Gain

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

32

THD+N versus Frequency

0.00001

0.0001

0.001

0.01

10 100 1,000 10,000 100,000Frequency (Hz)

TH

D+

N (

%)

Closed Loop Gain = 1 Closed Loop Gain = 10

THD+N 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

33THD+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.

34

THD+N versus FrequencySlew Rate Induced Distortion Full Power Bandwidth and Slew Rate

)( tVpSinVout

)( tVpCosSR f 2

VpfSR 2

If the output signal is given by:

after deviating we have:

where

The maximum slew rate occurs when the cosine term is 1. Thus, we have:

375kHz

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

Then slew rate is:

)( tVpSindt

d

dt

dVSR out

35

THD+N versus FrequencySlew 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.

36

THD+N versus FrequencyPratical 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+

37



2. Select amplifier with low THD, high Aol at frequencies of operation, and high slew rate.


4. Reduce loading as much as possible on the amplifier, it hurts Aol.

3. Minimize gains. Lower closed-loop gain means higher loop gain

-

+

R1 RF

RS

+

RLoad

+V s

R LO A D R LO A D

+V s

-Vs-Vs

38






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.


dt

dILV

39


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





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.


40

Summary

Types of distortion:1. Noise dominated distortion2. Gain roll-off induced distortion3. Slew induced distortion4. Practical tips

Things to look forward to:1. THD+N versus Amplitude plots and their significance2. 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

41

THD+N versus Frequency

Back up slides

42THD+N versus FrequencyTHD Dominated Region Closed Loop Gain and Distortion

OL

OLCL A

AA

1

GOL

OLG

G

OL

OLCL NA

AN

N

AA

A

1

OL

G

GCL

A

N

NA

1

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

• 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::

, 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.

Date post:	31-Dec-2015
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Harmonic Distortion versus Frequency in Amplifiers

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