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1 Harmonic Distortion versus Frequency in Amplifiers By Jorge Vega – Characterization Engineer & Raj Ramanathan – Design Engineer Precision Analog – Linear products – Op Amps 2 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 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+N Tool Blocks Tool of choice in industry: Audio Precision ~ 27k$ General tool blocks: 1. 2. 3. 4. 5. 6. 1 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 2 3 4 5 6 6 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 7 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 (%) n2 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% 8 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 9 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. 10 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 11 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. 12 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 (%) n2 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 13 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% 14 15 THD+N versus Frequency Noise Dominated Region Source Resistance effect on Noise THD+N is affected by the source resistance: - - + + RSource 16 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 17 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 18 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? 19 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 20 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” 21 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. 22 23 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 (%) n2 2 N V12 2 NOISE 100 THD+N versus Frequency THD Dominated Region Example 3: Find THD THD (%) 4 n2 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, 1.725E 07Vrms Thus we have: THD (%) (9.921E 07) 2 (6.267 E 07) 2 (1.725 E 07) 2 100 12 THD (%) 0.000118% • Shows that at 10kHz, measurement is THD dominated. • What happens if add noise? 0.000126% 24 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 4 THD N (%) THD N (%) n2 2 N 2 1 2 Noise V 2 V22 V32 V42 VNoise 100 100 V12 (9.921E 07) 2 (6.267 E 07) 2 (1.725E 07) 2 (0.42 E 06) 2 100 12 THD N (%) 0.000126% Matches! 0.000126% 25 26 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 27 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 28 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 29 30 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? 31 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 32 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 33 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. 34 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 35 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. 36 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 37 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 38 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 39 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. 40 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 41 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. 42