SECtIon 8 DISTORTION MEASUREMENTS High Speed Op Amp Distorti High Frequency Two-Tone generati Using Spectrum Analyzers in High Low Distortion measurements Measuring ADC Distortion using FFTS FFT Testing Troubleshooting the FFT Output nalyzing the FFT Or
1 SECTION 8 DISTORTION MEASUREMENTS High Speed Op Amp Distortion High Frequency Two-Tone Generation Using Spectrum Analyzers in High Frequency Low Distortion Measurements Measuring ADC Distortion using FFTs FFT Testing Troubleshooting the FFT Output Analyzing the FFT Output
section 8 DISTORTION MEASUREMENTS HIGH SPEED OP AMP DISTORTION Walt Kester Dynamic range of an op amp may be defined in several ways. The most common ways are to specify Harmonic Distortion, Total Harmonic Distortion (THD), or Total Harmonic Distortion Plus Noise (THD+N amp in a defined circuit configuration and observing the output spectrum. he op Harmonic distortion is measured by applying a spectrally pure sinewave to an op mount of distortion present in the output is usually a function of several parameters: the small- and large-signal nonlinearity of the amplifier being tested, the amplitude and frequency of the input signal, the load applied to the output of the amplifier, the amplifier's power supply voltage, printed circuit board layout grounding, power supply decoupling, etc. Therefore, any distortion specification is relatively meaningless unless the exact test conditions are specified. Harmonic distortion may be measured by looking at the output spectrum on a spectrum analyzer and observing the values of the second, third, fourth, etc harmonics with respect to the amplitude of the fundamental signal. The value is usually expressed as a ratio in % ppm, dB, or dBc. For instance, 0.0015% distortion corresponds to 15ppm, or-965dBc. The unit"dBc"simply means that the harmonic s level is so many db below the value of the"carrier"frequency, i.e., the fundamental Harmonic distortion may be expressed individually for each component (usually only the second and third are specified), or they all may be combined in a root-sum quare(RSS) fashion to give the Total Harmonic Distortion(THD). The distortion component which makes up Total Harmonic Distortion is usually calculated by taking the root sum of the squares of the first five or six harmonics of the fundamental. In many practical situations, however, there is negligible error if onl the second and third harmonics are included. This is because the rss process causes the higher-order terms to have negligible effect on the thD, if they are 3 to 5 times smaller than the largest harmonic. For example /0102+0032=√00109=010401
2 SECTION 8 DISTORTION MEASUREMENTS HIGH SPEED OP AMP DISTORTION Walt Kester Dynamic range of an op amp may be defined in several ways. The most common ways are to specify Harmonic Distortion, Total Harmonic Distortion (THD), or Total Harmonic Distortion Plus Noise (THD + N). Harmonic distortion is measured by applying a spectrally pure sinewave to an op amp in a defined circuit configuration and observing the output spectrum. The amount of distortion present in the output is usually a function of several parameters: the small- and large-signal nonlinearity of the amplifier being tested, the amplitude and frequency of the input signal, the load applied to the output of the amplifier, the amplifier's power supply voltage, printed circuit board layout, grounding, power supply decoupling, etc. Therefore, any distortion specification is relatively meaningless unless the exact test conditions are specified. Harmonic distortion may be measured by looking at the output spectrum on a spectrum analyzer and observing the values of the second, third, fourth, etc., harmonics with respect to the amplitude of the fundamental signal. The value is usually expressed as a ratio in %, ppm, dB, or dBc. For instance, 0.0015% distortion corresponds to 15ppm, or –96.5dBc. The unit "dBc" simply means that the harmonic's level is so many dB below the value of the "carrier" frequency, i.e., the fundamental. Harmonic distortion may be expressed individually for each component (usually only the second and third are specified), or they all may be combined in a root-sumsquare (RSS) fashion to give the Total Harmonic Distortion (THD). The distortion component which makes up Total Harmonic Distortion is usually calculated by taking the root sum of the squares of the first five or six harmonics of the fundamental. In many practical situations, however, there is negligible error if only the second and third harmonics are included. This is because the RSS process causes the higher-order terms to have negligible effect on the THD, if they are 3 to 5 times smaller than the largest harmonic. For example, 010 2 0032 . + . = 00109 . = 0104 . » 01
DEFINITIONS OF THD AND THD + N H Vs= Signal Amplitude(rms volts) V2= Second Harmonic Amplitude(rms volts) a Vn =nth Harmonic Amplitude(rms volts) a Vnoise =rms value of noise over measurement bandwidth THD+N= 2+v32+v42++2+ Voles v2+v2+v42++vn2 THD= Figure 8. 1 It is important to note that the THD measurement does not include noise terms while THD+ n does. The noise in the THD+N measurement must be integrated over the measurement bandwidth In audio applications, the bandwidth is normally chosen to be around 100kHz. In narrow-band applications, the level of the noise may be reduced by filtering. On the other hand, harmonics and intermodulation products which fall within the measurement bandwidth cannot be filtered, and therefore may limit the system dynamic range. It should be evident that the THD+N approximately equals THd if the rms noise over the measurement bandwidth is several times less than the THD, or even the worst harmonic. It is worth noting that if you know only the THD, you can calculate the THD+N fairly accurately using the amplifier's voltage- and current-noise specifications. Thermal noise associated with the source resistance and the feedback network may also need to be computed) But if the rms noise level is significantly higher than the level of the harmonics, and you are only given the THD+N specification, you cannot compute the ThD Special equipment is often used in audio applications for a more sensitive measurement of the noise and distortion. This is done by first using a bandstop filter to remove the fundamental signal (this is to prevent overdrive distortion in the measuring instrument). The total rms value of all the other frequency components (harmonics and noise) is then measured over an appropriate bandwidth. The ratio to the fundamental is the THD+N specification Audio frequency amplifiers(such as the OP-275)are optimized for low noise and low distortion within the audio bandwidth(20Hz to 20kHz). In audio applications, total harmonic distortion plus noise(THD+N) is usually measured with specialized equipment, such as the audio Precision System One. The output signal amplitude is measured at a given frequency(e. g. 1kHz); then the fundamental signal is removed with a bandstop filter, and the system measures the rms value of the remaining frequency components, which contain both harmonics and noise. The noise and harmonics are measured over a bandwidth that will include the highest harmonics
3 DEFINITIONS OF THD AND THD + N Figure 8.1 It is important to note that the THD measurement does not include noise terms, while THD + N does. The noise in the THD + N measurement must be integrated over the measurement bandwidth. In audio applications, the bandwidth is normally chosen to be around 100kHz. In narrow-band applications, the level of the noise may be reduced by filtering. On the other hand, harmonics and intermodulation products which fall within the measurement bandwidth cannot be filtered, and therefore may limit the system dynamic range. It should be evident that the THD+N approximately equals THD if the rms noise over the measurement bandwidth is several times less than the THD, or even the worst harmonic. It is worth noting that if you know only the THD, you can calculate the THD+N fairly accurately using the amplifier's voltage- and current-noise specifications. (Thermal noise associated with the source resistance and the feedback network may also need to be computed). But if the rms noise level is significantly higher than the level of the harmonics, and you are only given the THD+N specification, you cannot compute the THD. Special equipment is often used in audio applications for a more sensitive measurement of the noise and distortion. This is done by first using a bandstop filter to remove the fundamental signal (this is to prevent overdrive distortion in the measuring instrument). The total rms value of all the other frequency components (harmonics and noise) is then measured over an appropriate bandwidth. The ratio to the fundamental is the THD+N specification. Audio frequency amplifiers (such as the OP-275) are optimized for low noise and low distortion within the audio bandwidth (20Hz to 20kHz). In audio applications, total harmonic distortion plus noise (THD+N) is usually measured with specialized equipment, such as the Audio Precision System One. The output signal amplitude is measured at a given frequency (e.g., 1kHz); then the fundamental signal is removed with a bandstop filter, and the system measures the rms value of the remaining frequency components, which contain both harmonics and noise. The noise and harmonics are measured over a bandwidth that will include the highest harmonics
usually about 100kHz. The measurement is swept over the frequency range for various conditions THD+N results for the OP-275 are plotted in Figure 8.2 as a function of frequency The signal level is 3V rms, and the amplifier is connected as a unity-gain follower The data is shown for three load conditions: 600ohm. 2kohm. and 10kohm. Notice that a THD+N value of.0008% corresponds to 8ppm, or-102dBc. The input voltage noise of the OP-275 is typically 6n V/rtHz@ 1kHz, and integrated over an 80kHz noise bandwidth, yields an rms noise level of 1.7uV rms For a 3V rms signal level the corresponding signal-to-noise ratio is 125dB. Because the THd is considerably greater than the noise level, the THD component is the primary contributor. Multiple plots with variable bandwidths can be used to help separate noise and distortion THD N FOR THE OP-275 OVER 100kHz BANDWIdTH IS DOMINATED BY DISTORTION RL=600.2K,10k FREQUENCY-Hz Figure 8.2 Now, consider the AD797, a low noise amplifier(Inv/rtHz) where measurement equipment distortion, and not the amplifier distortion, limits the measurement The ID specification for the AD797 is 120dBc@ 20kHz, and a plot is shown in Figure 8.3. The distortion is at the limits of measurement of available equipment, and the actual amplifier noise is even lower by 20dB. The measurement was made with a spectrum analyzer by first filtering out the fundamental sinewave frequency ahead first five harmonics were then measured and combined in an RSS fashion to get the of the analyzer. This is to prevent overdrive distortion in the spectrum analyzer. The THD figure. The legend on the graph indicates that the measurement equipment floor"is about 120dBe; hence at frequencies below 10kHz, the THD may be even
4 usually about 100kHz. The measurement is swept over the frequency range for various conditions. THD+N results for the OP-275 are plotted in Figure 8.2 as a function of frequency. The signal level is 3V rms, and the amplifier is connected as a unity-gain follower. The data is shown for three load conditions: 600ohm, 2kohm, and 10kohm. Notice that a THD+N value of 0.0008% corresponds to 8ppm, or –102dBc. The input voltage noise of the OP-275 is typically 6nV/rtHz @ 1kHz, and integrated over an 80kHz noise bandwidth, yields an rms noise level of 1.7µV rms. For a 3V rms signal level, the corresponding signal-to-noise ratio is 125dB. Because the THD is considerably greater than the noise level, the THD component is the primary contributor. Multiple plots with variable bandwidths can be used to help separate noise and distortion. THD + N FOR THE OP -275 OVER 100kHz BANDWIDTH IS DOMINATED BY DISTORTION Figure 8.2 Now, consider the AD797, a low noise amplifier (1nV/rtHz) where measurement equipment distortion, and not the amplifier distortion, limits the measurement. The THD specification for the AD797 is 120dBc @ 20kHz, and a plot is shown in Figure 8.3. The distortion is at the limits of measurement of available equipment, and the actual amplifier noise is even lower by 20dB. The measurement was made with a spectrum analyzer by first filtering out the fundamental sinewave frequency ahead of the analyzer. This is to prevent overdrive distortion in the spectrum analyzer. The first five harmonics were then measured and combined in an RSS fashion to get the THD figure. The legend on the graph indicates that the measurement equipment "floor" is about 120dBc; hence at frequencies below 10kHz, the THD may be even less
THD OF THE AD797 OP AMP SHOWS MEASUREMENT LIMIT AT-120dBC, WHILE AMPLIFIER NOISE FLOOR IS AT -140dBc (1nV/Hz INTEGRATED OVER 100kHz BANDWIDTH) VOLTAGE NOISE THD Figure 8.3 To calculate the AD797 noise, multiply the voltage noise spectral density(In v/rtHz by the square root of the measurement bandwidth to yield the device 's rms noise floor. For a 100kHz bandwidth, the noise floor is 316nV rms, corresponding to a signal-to-noise ratio of about 140dB for a 3V rms output signal Rather than simply examining the Thd produced by a single tone sinewave input, it is often useful to look at the distortion products produced by two tones. As shown in Figure 8.4, two tones will produce second and third order intermodulation products. The example shows the second and third order products produced by applying two frequencies, f1 and f2, to a nonlinear device. The second order products located at f2 +fi and f2-f1 are located far away from the two tones, and may be removed by filtering. The third order products located at 2f1+ fo and 2f2 +fi may likewise be filtered. The third order products located at 2f1-fe and 2fo-f1, however, are close to the original tones, and filtering them is difficult. Third order IMD products are especially troublesome in multi-channel communications systems where the channel separation is constant across the frequency band
5 THD OF THE AD797 OP AMP SHOWS MEASUREMENT LIMIT AT -120dBc, WHILE AMPLIFIER NOISE FLOOR IS AT -140dBc (1nV/ Hz INTEGRATED OVER 100kHz BANDWIDTH) Figure 8.3 To calculate the AD797 noise, multiply the voltage noise spectral density (1nV/rtHz) by the square root of the measurement bandwidth to yield the device's rms noise floor. For a 100kHz bandwidth, the noise floor is 316nV rms, corresponding to a signal-to-noise ratio of about 140dB for a 3V rms output signal. Rather than simply examining the THD produced by a single tone sinewave input, it is often useful to look at the distortion products produced by two tones. As shown in Figure 8.4, two tones will produce second and third order intermodulation products. The example shows the second and third order products produced by applying two frequencies, f1 and f2, to a nonlinear device. The second order products located at f2 + f1 and f2 – f1 are located far away from the two tones, and may be removed by filtering. The third order products located at 2f1 + f2 and 2f2 + f1 may likewise be filtered. The third order products located at 2f1 – f2 and 2f2 – f1, however, are close to the original tones, and filtering them is difficult. Third order IMD products are especially troublesome in multi-channel communications systems where the channel separation is constant across the frequency band
SECOND AND THIRD-ORDER INTERMODULATION PRODUCTS FOR f,= 5MHz and f,= 6MHz 2=SECOND ORDER IMD PRODUCTS (3=THIRD ORDER IMD PRODUCTS NOTE: f1=5MHz, f2=6MHz 101112 FREQUENCY: MHz Figure 8.4 Intermodulation distortion products are of special interest in the rF area, and a major concern in the design of radio receivers. Third-order IMd products can mask out small signals in the presence of larger ones. Third order IMD is often specified in terms of the third order intercept point as shown in Figure 8.5 two spectrally pure ones are applied to the system. The output signal power in a single tone (in dBm)as well as the relative amplitude of the third-order products (referenced to a single tone)is plotted as a function of input signal power. If the system non-linearity is approximated by a power series expansion, the second-order IMd amplitudes increase 2dB for every 1dB of signal increase. Similarly, the third-order IMD ldB of sig With a low level two-ton input signal, and two data points, draw the second and third order Imd lines as are shown in Figure 8.5, because one point and a slope determine each straight line Once the input reaches a certain level, however, the output signal begins to soft limit, or compress. But the second and third-order intercept lines may be extended to intersect the extension of the output signal line. These intersections are called the second-and third order intercept points, respectively. The values are usually referenced to the output power of the device expressed in dBm. Another parameter which may be of interest is the 1dB compression point. This is the point at which the output signal is compressed by 1dB from the ideal input/output transfer function This point is also shown in Figure 8.5
6 SECOND AND THIRD-ORDER INTERMODULATION PRODUCTS FOR f1 = 5MHz and f2 = 6MHz Figure 8.4 Intermodulation distortion products are of special interest in the RF area, and a major concern in the design of radio receivers. Third-order IMD products can mask out small signals in the presence of larger ones. Third order IMD is often specified in terms of the third order intercept point as shown in Figure 8.5. Two spectrally pure tones are applied to the system. The output signal power in a single tone (in dBm) as well as the relative amplitude of the third-order products (referenced to a single tone) is plotted as a function of input signal power. If the system non-linearity is approximated by a power series expansion, the second-order IMD amplitudes increase 2dB for every 1dB of signal increase. Similarly, the third-order IMD amplitudes increase 3dB for every 1dB of signal increase. With a low level two-tone input signal, and two data points, draw the second and third order IMD lines as are shown in Figure 8.5, because one point and a slope determine each straight line. Once the input reaches a certain level, however, the output signal begins to softlimit, or compress. But the second and third-order intercept lines may be extended to intersect the extension of the output signal line. These intersections are called the second- and third order intercept points, respectively. The values are usually referenced to the output power of the device expressed in dBm. Another parameter which may be of interest is the 1dB compression point. This is the point at which the output signal is compressed by 1dB from the ideal input/output transfer function. This point is also shown in Figure 8.5. I
NTERCEPT POINTS, GAIN COMPRESSION, AND IMD SECOND ORDEI INTERCEPT OUTPUT r THIRD OHDER 1 6B COMPRESSION FUNDAMENTA oFn INPUT POWER (PER TONE, dBm Figure 8.5 Knowing the third order intercept point allows calculation of the approximate level of the third-order Imd products as a function of output signal level Figure 8.6 shows the third order intercept value as a function of frequency for the AD9622 voltage feedback amplifier
7 NTERCEPT POINTS, GAIN COMPRESSION, AND IMD Figure 8.5 Knowing the third order intercept point allows calculation of the approximate level of the third-order IMD products as a function of output signal level. Figure 8.6 shows the third order intercept value as a function of frequency for the AD9622 voltage feedback amplifier
AD9622 THIRD ORDER IMD INTERCEPT VERSUS FREQUENCY to。UT +-au 10 100 FREQUENCY-MHz Figure 8.6 Assume the op amp output signal is 5MHz and 2v peak-to-peak into a 100ohm load (50ohm source and load termination). The voltage into the 50ohm load is therefore 1V peak-to-peak, corresponding to +4dBm. The value of the third order intercept at 5MHz is 36dBm. The difference between +36dBm and +dbM is 32dB. This value is then multiplied by 2 to yield 64db (the value of the third-order intermodulation products referenced to the power in a single tone). Therefore, the intermodulation products should be -64dBe(dB below carrier frequency), or at a level of-60dBm Figure 8.7 shows the graphical analysis for this example
8 AD9622 THIRD ORDER IMD INTERCEPT VERSUS FREQUENCY Figure 8.6 Assume the op amp output signal is 5MHz and 2V peak-to-peak into a 100ohm load (50ohm source and load termination). The voltage into the 50ohm load is therefore 1V peak-to-peak, corresponding to +4dBm. The value of the third order intercept at 5MHz is 36dBm. The difference between +36dBm and +4dBm is 32dB. This value is then multiplied by 2 to yield 64dB (the value of the third-order intermodulation products referenced to the power in a single tone). Therefore, the intermodulation products should be –64dBc (dB below carrier frequency), or at a level of –60dBm. Figure 8.7 shows the graphical analysis for this example
USING THE THIRD ORDER INTERCEPT POINT TO CALCULATE IMD PRODUCT FOR THE AD9622 OP AMP OUTPUT +20 POWER RD ORDER IMD e.Odam NPUT POWER (PER TONE), dB Figure 8.7 HIGH FREQUENCY TWO-TONE GENERATION Generating test signals with the spectral purity required to make low distortion high frequency measurements is a challenging task. a test setup for generating a single tone is shown in Figure8.8. The sinewave oscillator should have low phase noise output. The distortion should be GdB lower than the desired accuracy ottho cillata (e. g, Marconi 2382), especially if the device under test is an ADC, where phase nois increases the ADC noise floor. The output of the oscillator is passed through a bandpass(or lowpass) filter which removes any harmonics present in the os measurement. The 6dB attenuator isolates the dut from the output of the filter. The impedance at each interface should be maintained at 50ohms for best performance(75ohm components can be used, but 50ohm attenuators and filters are generally more readily available). The termination resistor, RT, is selected so that the parallel combination of rr and the input impedance of the dut is 50ohms LOW DISTORTION SINGLE-TONE GENERATOR NALYZER INPUT OSCILLATO ATTEN Figure 8.8
9 USING THE THIRD ORDER INTERCEPT POINT TO CALCULATE IMD PRODUCT FOR THE AD9622 OP AMP Figure 8.7 HIGH FREQUENCY TWO-TONE GENERATION Generating test signals with the spectral purity required to make low distortion high frequency measurements is a challenging task. A test setup for generating a single tone is shown in Figure 8.8. The sinewave oscillator should have low phase noise (e.g., Marconi 2382), especially if the device under test is an ADC, where phase noise increases the ADC noise floor. The output of the oscillator is passed through a bandpass (or lowpass) filter which removes any harmonics present in the oscillator output. The distortion should be 6dB lower than the desired accuracy of the measurement. The 6dB attenuator isolates the DUT from the output of the filter. The impedance at each interface should be maintained at 50ohms for best performance (75ohm components can be used, but 50ohm attenuators and filters are generally more readily available). The termination resistor, RT, is selected so that the parallel combination of RT and the input impedance of the DUT is 50ohms. LOW DISTORTION SINGLE-TONE GENERATOR Figure 8.8
Before performing the actual distortion measurement, the oscillator output should be set to the correct frequency and amplitude. Measure the distortion at the output of the attenuator with the dut replaced by a 50ohm termination resistor(generally the 50ohm input of a spectrum analyzer. Next, replace the 50ohm load with RT and the DUT. Measure the distortion at the dut input a second time. This allows non- linear dUT loads to be identified. Non-linear DUT loads(such as flash ADCs with signal-dependent input capacitance, or switched-capacitor CMOS ADCs)can introduce distortion at the dut input Generating two tones suitable for IMD measurements is even more difficult. A low distortion two-tone generator is shown in Figure 8.9. Two bandpass(or lowpass filters are required as shown. Harmonic suppression of each filter must be better than the desired measurement accuracy by at least 6dB. a 6dB attenuator at the output of each filter serves to isolate the filter outputs from each other and prevent possible cross-modulation. The outputs of the attenuators are combined in a passive 50ohm combining network, and the combiner drives the dut. The oscillator outputs are set to the required level, and the imd of the final output of the combiner is measured. The measurement should be made with a single termination resistor, and again with the dut connected to identify non-linear load OW DISTORTION TOW TONE GENERATOR INPUT EWAVE Figure 8.9 USING SPECTRUM ANALYZERS IN HIGH FREQUENCY LOW DISTORTION MEASUREMENTS Analog spectrum analyzers are most often used to measure amplifier distortion. Most have 50ohm inputs, therefore an isolation resistor between the device under test dut) and the analyzer is required to simulate duT loads greater than 50ohms After adjusting the spectrum analyzer for bandwidth, sweep rate and sensitivity check it carefully for input overdrive. The simplest method is to use the variable attenuator to introduce 10dB of attenuation in the analyzer input path. both the signal and any harmonics should be attenuated by a fixed amount(10dB, for instance)as observed on the screen of the spectrum analyzer. If the harmonics are attenuated by more than 10dB, then the input amplifier of the analyzer is introducing distortion, and the sensitivity should be reduced. Many analyzers have a
1 0 Before performing the actual distortion measurement, the oscillator output should be set to the correct frequency and amplitude. Measure the distortion at the output of the attenuator with the DUT replaced by a 50ohm termination resistor (generally the 50ohm input of a spectrum analyzer. Next, replace the 50ohm load with RT and the DUT. Measure the distortion at the DUT input a second time. This allows nonlinear DUT loads to be identified. Non-linear DUT loads (such as flash ADCs with signal-dependent input capacitance, or switched-capacitor CMOS ADCs) can introduce distortion at the DUT input. Generating two tones suitable for IMD measurements is even more difficult. A lowdistortion two-tone generator is shown in Figure 8.9. Two bandpass (or lowpass) filters are required as shown. Harmonic suppression of each filter must be better than the desired measurement accuracy by at least 6dB. A 6dB attenuator at the output of each filter serves to isolate the filter outputs from each other and prevent possible cross-modulation. The outputs of the attenuators are combined in a passive 50ohm combining network, and the combiner drives the DUT. The oscillator outputs are set to the required level, and the IMD of the final output of the combiner is measured. The measurement should be made with a single termination resistor, and again with the DUT connected to identify non-linear loads. LOW DISTORTION TOW TONE GENERATOR Figure 8.9 USING SPECTRUM ANALYZERS IN HIGH FREQUENCY LOW DISTORTION MEASUREMENTS Analog spectrum analyzers are most often used to measure amplifier distortion. Most have 50ohm inputs, therefore an isolation resistor between the device under test (DUT) and the analyzer is required to simulate DUT loads greater than 50ohms. After adjusting the spectrum analyzer for bandwidth, sweep rate, and sensitivity, check it carefully for input overdrive. The simplest method is to use the variable attenuator to introduce 10dB of attenuation in the analyzer input path. Both the signal and any harmonics should be attenuated by a fixed amount (10dB, for instance) as observed on the screen of the spectrum analyzer. If the harmonics are attenuated by more than 10dB, then the input amplifier of the analyzer is introducing distortion, and the sensitivity should be reduced. Many analyzers have a
