Application Report SBOA110A – June 2005 – Revised November 2005 PGA309 Noise Filtering Art Kay............................................................................................. High-Performance Linear Products ABSTRACT The PGA309 programmable gain amplifier generates three primary types of noise: broadband noise, noise from the instrumentation amplifier auto-zero circuit, and noise from the Coarse Offset auto-zero circuit. Noise at the PGA309 output can be reduced by limiting the bandwidth with a simple filter. This application note describes how to select the filter components in order to get the desired bandwidth, and how to mathematically estimate the amount of output noise based on the circuit configuration. Components that improve RFI and EMI immunity are also described. Contents 1 Selecting Components for the Output Filter ..................................................... 2 2 Understanding the Noise Spectrum of Auto-Zero Amplifiers ................................. 3 3 Estimating PGA309 Noise Output for a Given Design......................................... 5 4 RFI and EMI ....................................................................................... 10 Appendix A Measurement Results .................................................................. 11 List of Figures 1 2 3 4 5 6 7 8 9 A-1 A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 A-10 A-11 A-12 A-13 A-14 A-15 A-16 PGA309 with Simple Single Post Filter .......................................................... 2 PGA309 Noise Spectrum .......................................................................... 4 PGA309 Noise Spectrum with Maximum Coarse Offset (–59mV) ........................... 5 PGA309 Noise Density (1kHz Filter Superimposed) ........................................... 6 Low-Pass Filter Brick Wall Filter Equivalents ................................................... 6 PGA309 Noise Density (10kHz Filter Superimposed) ......................................... 8 Broadband (White) Noise, Coarse Offset = 0V ................................................. 9 Noise with Maximum Coarse Offset ............................................................ 10 Noise Generated with Improperly Decoupled Digital Source ................................ 10 Noise with 100Hz Filter, No Coarse Offset .................................................... 11 Noise Measurement .............................................................................. 11 Noise with 100Hz Filter, Maximum Coarse Offset ............................................ 12 Noise Measurement .............................................................................. 12 Noise with 1kHz Filter, No Coarse Offset ...................................................... 13 Noise Measurement .............................................................................. 13 Noise with 1kHz Filter, Maximum Coarse Offset.............................................. 14 Noise Measurement .............................................................................. 14 Noise with 10kHz Filter, No Coarse Offset .................................................... 15 Noise Measurement .............................................................................. 15 Noise with 10kHz Filter, Maximum Coarse Offset ............................................ 16 Noise Measurement .............................................................................. 16 Noise with Maximum Bandwidth, No Coarse Offset .......................................... 17 Noise Measurement .............................................................................. 17 Noise with Maximum Bandwidth, Maximum Coarse Offset ................................. 18 Noise Measurement .............................................................................. 18 All trademarks are the property of their respective owners. SBOA110A – June 2005 – Revised November 2005 PGA309 Noise Filtering 1 www.ti.com Selecting Components for the Output Filter 1 Selecting Components for the Output Filter The circuit shown in Figure 1 illustrates how the output amplifier can be used to create a simple single pole filter. The capacitor CF in parallel with the internal feedback resistor RFO forms the filter. Table 1 lists the values of RFO for different gain settings. Table 1 also lists the nearest standard capacitor value for CF to obtain bandwidths of 100Hz, 1kHz, and 10kHz. The CF value required to obtain bandwidths not listed in Table 1 can be calculated as shown in Example 1. In addition, this configuration allows for a 10nF RFI/EMI capacitor, CL, to be directly between the output and ground of a module. C3 0.01µF C2 0.1µF VSA VSD PGA309 Output Amplifier SDA SCL Two−Wire EEPROM C1 0.01µF Front End PGA VS (Gain DAC) Output Amp INT/EXT FB Select RFO Allows for other Output Amplifier External Gain Settings R ISO 100Ω V OUT V OUT FILT RF B 100Ω V FB CL 10nF GND Output Gain Select X2, X2.4, X3, X3.6, X4.5, X6, X9 RFO CF V SJ VSA V SA Figure 1. PGA309 with Simple Single Post Filter 2 PGA309 Noise Filtering SBOA110A – June 2005 – Revised November 2005 www.ti.com Understanding the Noise Spectrum of Auto-Zero Amplifiers Table 1. PGA309 Low Noise Filter Values at Different Gains DESIRED BANDWIDTH OUTPUT AMP GAIN RFO (kΩ) CF COMPUTED (F) CF STANDARD 100Hz 2 18 8.842E–08 0.091µF 100Hz 2.4 21 7.579E–08 0.075µF 100Hz 3 24 6.631E–08 0.068µF 100Hz 3.6 26 6.121E–08 0.062µF 100Hz 4.5 28 5.684E–08 0.056µF 100Hz 6 30 5.305E–08 0.051µF 100Hz 9 32 4.974E–08 0.047µF . 1kHz 2 18 8.842E–09 9100pF 1kHz 2.4 21 7.579E–09 7500pF 1kHz 3 24 6.631E–09 6800pF 1kHz 3.6 26 6.121E–09 6200pF 1kHz 4.5 28 5.684E–09 5600pF 1kHz 6 30 5.305E–09 5100pF 1kHz 9 32 4.974E–09 4700pF 10kHz 2 18 8.842E–10 910pF 10kHz 2.4 21 7.579E–10 750pF 10kHz 3 24 6.631E–10 680pF 10kHz 3.6 26 6.121E–10 620pF 10kHz 4.5 28 5.684E–10 560pF 10kHz 6 30 5.305E–10 510pF 10kHz 9 32 4.974E–10 470pF Example 1. Calculation to Select CF Value For this example, we want to design a circuit with a gain of 4.5 and a bandwidth of 3kHz. When the gain is set to 4.5, the feedback resistor is equal to RFO = 28kΩ. The value of CF is computed as shown: 1 CF 2 BW RFO (1) 1 CF 1.895nF 2 (3kHz) (28k) (2) Use a standard 2nF value resistor. 2 Understanding the Noise Spectrum of Auto-Zero Amplifiers When considering the noise generated by the PGA309, it is important to keep in mind that it uses auto-zero amplifiers in the programmable gain instrumentation amplifier (PGIA). The auto-zero technique has some interesting effects on the noise spectrum of an amplifier. One beneficial effect of the auto-zero architecture is that it eliminates 1/f noise (flicker noise). Typically, it accomplishes this at the cost of increasing the overall broadband noise. For applications where the bandwidth can be limited, the overall output noise will typically be lower for auto-zero topologies. Figure 2 illustrates the spectrum of the PGA309 (with no 1/f noise). SBOA110A – June 2005 – Revised November 2005 PGA309 Noise Filtering 3 www.ti.com Understanding the Noise Spectrum of Auto-Zero Amplifiers The cut frequency of the noise spectrum is at the auto−zero frequency (approximately 7kHz). Also, there are noise components are at the auto−zero frequency and its harmonic. INPUT VOLTAGE NOISE DENSITY 1 eND (µV/√Hz), RTI Coarse Offset Adjust = 0mV CLK_CFG = ’00’ (default) 0.1 0.01 1 10 100 1k 10k 100k Frequency (Hz) Referred to the input, the noise spectral density is 210nV/√Hz. After the corner frequency, the noise spectrum drops to about 20nV/√Hz to 40nV/√Hz. Figure 2. PGA309 Noise Spectrum The auto-zero technique also shapes the noise spectrum in other ways. The noise spectrum for the PGA309 is a flat 210nV/√Hz from 0Hz to approximately 8kHz. The corner frequency of the noise spectrum is set by the auto-zero frequency. For the PGA309, the auto-zero frequency is between 7kHz and 8kHz. After the corner frequency, the noise spectrum drops to about 20nV/√Hz to 40nV/√Hz. Typically, there will be noise components at the auto-zero frequency and at harmonics of the auto-zero frequency. For an auto-zero frequency of 8kHz, you will see noise components at 8kHz, 16kHz, 24kHz, 40kHz, 56kHz, and at other harmonics in 8kHz multiples. The PGA309 also has a Coarse Offset Digital-to-Analog Converter (DAC) that is used to compensate for the large initial offset of the sensor. When the Coarse Offset is not being used, the noise is dominated by the flat broadband (210nV/√Hz) noise, and the magnitude of the auto-zero clock harmonics is not a factor. The Coarse Offset DAC, however, has a different auto-zero scheme that has feed-through which may need to be considered. The Coarse Offset DAC has an auto-zero frequency that is half of the auto-zero frequency of the PGIA (typically, 3.5kHz to 4kHz). Figure 3 shows the noise spectrum of the PGA309 with the output of the Coarse Offset DAC set to maximum. 4 PGA309 Noise Filtering SBOA110A – June 2005 – Revised November 2005 www.ti.com Estimating PGA309 Noise Output for a Given Design When the PGA309 coarse offset feature is used, the noise components at the auto−zero frequency and its harmonics may be larger. The auto−zero frequency of the Coarse−Offset DAC is 3.5kHz to 4kHz. INPUT VOLTAGE NOISE DENSITY eND (µV/√Hz), RTI 10 Coarse Offset Adjust = −59mV VIN = +61mV CLK_CFG = ’00’ (default) 1 0.1 0.01 1 10 100 1k 10k 50k Frequency (Hz) Figure 3. PGA309 Noise Spectrum with Maximum Coarse Offset (–59mV) 3 Estimating PGA309 Noise Output for a Given Design The noise output on the PGA309 is a factor of gain, bandwidth, and amount of coarse offset used. To minimize output noise, you should set your bandwidth to the smallest level that will work for your specific application. Also, in many cases, it is possible to minimize the coarse offset by using the Zero DAC to compensate for the large initial offset of the sensor. A good way of understanding the trade-off between the Coarse Offset setting and Zero DAC is to use the PGA309 Gain Calculator software tool. This calculator can be downloaded via the PGA309 product folder on the TI web site, under Software Tools. It is described in detail in the PGA309EVM User's Guide. The first step to determine the noise output of the PGA309 is to estimate the broadband noise of the PGA309. In order to perform this calculation, you need to know the gain and bandwidth requirement for the particular design. Then, you will calculate the output peak-to-peak noise. Section 3.1 reviews how to compute the output peak-to-peak noise based on the broadband spectrum noise. 3.1 Computing the Output Peak-to-Peak Noise Based on the Broadband Spectrum In general, the total root mean squared (RMS) noise referred to the input of an amplifier can be computed by integrating the spectral noise density curve. In most cases, however, there are some simple formulas that can be used to simplify this computation. Figure 4 shows the PGA309 noise spectral density with a simple 1kHz filter superimposed on it. For this example, only the noise inside the 1kHz filter is integrated to get the total noise. There are two regions of the graph that affect the result. The region from 0Hz to 1kHz is rectangular; consequently, it lends itself well to a simple formula (area = length x width). The region beyond 1kHz depends on the type of filter used, and thus a table of correction factors Kn is developed based on the filter type. The correction factor effectively converts the filter to a brick wall filter so that the entire noise spectrum is rectangular (see Figure 5 and Table 2). SBOA110A – June 2005 – Revised November 2005 PGA309 Noise Filtering 5 www.ti.com Estimating PGA309 Noise Output for a Given Design When the bandwidth is limited using a 1kHz filter, only the noise inside the 1kHz bandwidth is integrated to compute the output noise. INPUT VOLTAGE NOISE DENSITY 1 eND (µV/√Hz), RTI Coarse Offset Adjust = 0mV CLK_CFG = ’00’ (default) 0.1 0.01 1 10 100 1k 10k 100k Frequency (Hz) The region from 0Hz to 1kHz can be integrated using a simple calculation. A correction factor (Kn) is used to compute include the noise in the region beyond 1kHz. The value of Kn depends on the order of the filter being used. Our example filter is first order and kn = 1.57. Figure 4. PGA309 Noise Density (1kHz Filter Superimposed) Noise BW Small−Signal BW 0 Filter Attenuation (dB) Skirt of 1−Pole Filter Response Skirt of 2−Pole Filter Response −20 Skirt of 3−Pole Filter Response −40 Brickwall −80 0.1fP 10fP fP f BF Frequency (f) Figure 5. Low-Pass Filter Brick Wall Filter Equivalents 6 PGA309 Noise Filtering SBOA110A – June 2005 – Revised November 2005 www.ti.com Estimating PGA309 Noise Output for a Given Design Table 2. Conversion From Standard Filter to Brick Wall Filter NUMBER OF POLES IN FILTER Kn AC NOISE BANDWIDTH RATIO 1 1.57 2 1.22 3 1.16 4 1.13 5 1.12 Example 2 in Section 3.2 illustrates how the noise calculation is performed. It should be emphasized, however, that the noise computed by integrating the spectral density curve is an RMS quantity. Most users are interested in the peak-to-peak noise. This noise has a normal distribution, and therefore, the peak-to-peak noise output can be estimated. Typically, the (RMS value x 6) is a good estimate of the peak-to-peak distribution. This practice is used because there is a probability of 0.3% that the peak-to-peak noise will exceed this level at a given instant in time. This factor is sometimes called the crest factor. Some engineers use different crest factors depending on whether they want to be more or less conservative with their estimates. Table 3 lists several crest factors and the associated probability that the signal will have a larger amplitude at a given instant in time. Table 3. Crest Factors Used to Convert RMS Noise to Peak-to-Peak Noise PEAK-TO-PEAK AMPLITUDE CREST FACTOR PROBABILITY OF HAVING A LARGER AMPLITUDE (%) 2 × RMS 2 32 3 × RMS 3 13 4 × RMS 4 4.6 5 × RMS 5 1.2 6 × RMS 6 0.3 7 × RMS 7 0.05 SBOA110A – June 2005 – Revised November 2005 PGA309 Noise Filtering 7 www.ti.com Estimating PGA309 Noise Output for a Given Design 3.2 Example 2: General Formulas for Computing Noise from a Broadband Source V noise_broadband Gain Noise_Density BW K n (3) V noise_peak_to_peak 6 V noise_broadband (4) Where: • Gain = Gain_of_PGIA × GAIN_DAC × Output_Amp_Gain Gain is the total gain of the PGA309 • Noise Density = 210nV/√Hz from 0Hz to 8kHz • BW = PGA309 Bandwidth. The bandwidth can be adjusted by using the appropriate value of CF as discussed in Section 1. • Kn = the brick wall filter multiplier to include the skirt effects of a low-pass filter. This factor is selected from Table 2, based on the type of filter that is used in the particular application. For our example design, we will choose: Gain (128) (1.0) (9) 1152 (5) This is the maximum gain for the PGA309 (worst-case noise). BW 1.0kHz Typical bandwidth (6) K n 1.57 This value is used because CF forms a first−order filter. (7) The noise output is then calculated: V 1152 210nV Hz (1.0kHz) (1.57) 29mV noise_broadband RMS (8) V noise_peak_to_peak 6 (0.029V RMS) 174mVPP 3.3 (9) Computing the Output Peak-to-Peak Noise Using the Broadband Spectrum When Bandwidth is Greater than Auto-Zero Frequency The method described in Section 3.1 works well when the filter bandwidth is less than the auto-zero frequency (7kHz and 8kHz). In cases where the bandwidth is greater than the auto-zero frequency, it becomes more difficult to estimate the noise because the spectral noise density of the PGA309 begins to roll off. (See Figure 6.) Table 4 lists measured results for several different configurations. These measured results provide an approximation of expected noise for wide bandwidth configurations. When the bandwidth is limited using a 10kHz filter, the resultant noise calculation becomes more complex because the noise roles off before the filter. INPUT VOLTAGE NOISE DENSITY 1 eND (µV/√Hz), RTI Coarse Offset Adjust = 0mV CLK_CFG = ’00’ (default) 0.1 0.01 1 10 100 1k 10k 100k Frequency (Hz) Figure 6. PGA309 Noise Density (10kHz Filter Superimposed) 8 PGA309 Noise Filtering SBOA110A – June 2005 – Revised November 2005 www.ti.com Estimating PGA309 Noise Output for a Given Design Table 4. Summary of Measured Results (1) (1) (2) (3) 3.4 FILTER COARSE OFFSET OUTPUT NOISE RMS OUTPUT NOISE CALCULATED (Example 1) 100Hz None 3.7mVRMS 2.88mVRMS 100Hz Max (–48mV) 8.7mVRMS 1kHz None 9mVRMS 1kHz Max (–48mV) 12.5mVRMS 10kHz None 17.8mVRMS 10kHz Max (–48mV) 42.1mVRMS 252mVPP None None 26.3mVRMS 157mVPP None Max (–48mV) 65.3mVRMS 391mVPP OUTPUT NOISE PEAK-TO-PEAK (CALCULATED FROM RMS SCOPE) (2) 22mVPP 52mVPP 9.12mVRMS 54mVPP 29mVRMS (3) 106mVPP 75mVPP All measurements made with Gain = 1125, VREF = 3.4V. For other gains, compute the output noise using this equation: VNOISE = (Gain)(Measured_Output_Noise)/1125 Crest factor = 6. Not accurate because of noise roll-off. Effect on PGA309 Coarse Offset Auto-Zero Feed through on Noise The PGA309 can compensate for the initial large offset of a sensor by using its Coarse Offset DAC. The Coarse Offset DAC uses the auto-zero technique (its auto-zero frequency is 3.5kHz to 4kHz). For large values of coarse offset, the auto-zero clock feed-through can be the dominant noise source. Since the noise generated by the auto-zero feed-through is not broadband noise, there is no simple formula to estimate this noise. The easiest way to get an approximate noise output for this effect is to examine the measured results. (See Table 4.) Keep in mind that the measured results will include both the broadband noise and the auto-zero feed-through. As a rule of thumb, the effects of auto-zero feed-through from coarse offset can double the noise from the PGA309 when coarse offset is set to maximum. 3.5 What to Expect on an Oscilloscope When the coarse offset is not used or set to a small level, broadband noise will dominate. This noise appears to be a random signal (or white noise) on the oscilloscope. (See Figure 7.) When coarse offset is set to a larger level, the auto-zero clock feed-through dominates. This signal looks like a noisy square wave with a frequency of 3.5kHz to 4kHz; see Figure 8. C1 RMS 26.3mV 50.0mV 5.00ms Figure 7. Broadband (White) Noise, Coarse Offset = 0V SBOA110A – June 2005 – Revised November 2005 PGA309 Noise Filtering 9 www.ti.com RFI and EMI 250kS/s 50.0mV C1 RMS 65.3mV 200µs Figure 8. Noise with Maximum Coarse Offset 4 RFI and EMI CL, RFB and RISO are used to prevent emission and reception RFI and EMI from the PGA309. These components are especially important if the PGA309 is being connected via cable to a measurement system. RFB and RISO also protect against incorrect wiring faults. C1, C2 and C3 are decoupling capacitors that keep the digital signals used to communicate to the EEPROM out of the analog. Figure 9 illustrates noise that you can see if you have not properly decoupled the PGA309; the noise glitches correspond to the edges of the SCL signal. 50MS/s Ch1PP 25.6mV Ch1 Freq 19.05MHz Low Res 20mV 1µs Figure 9. Noise Generated with Improperly Decoupled Digital Source 10 PGA309 Noise Filtering SBOA110A – June 2005 – Revised November 2005 www.ti.com Appendix A Appendix A Measurement Results PGA309 WITH AND WITHOUT 1kHz FILTER (Gain = 1152, Coarse Offset = 0mV) Noise Spectral Density (V/√Hz) 0.001 No Filter 0.0001 0.00001 1k Filter 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-1. Noise with 100Hz Filter, No Coarse Offset 250kS/s 10.0mV C1 RMS 3.74mV 200µs Figure A-2. Noise Measurement SBOA110A – June 2005 – Revised November 2005 Measurement Results 11 www.ti.com Appendix A PGA309 WITH AND WITHOUT 100Hz FILTER (Gain = 1152, Coarse Offset = 48mV) Noise Spectral Density (V/√Hz) 0.01 No Filter 0.001 0.0001 0.00001 100Hz 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-3. Noise with 100Hz Filter, Maximum Coarse Offset 250kS/s 10.0mV C1 RMS 8.50mV 200µs Figure A-4. Noise Measurement 12 Measurement Results SBOA110A – June 2005 – Revised November 2005 www.ti.com Appendix A PGA309 WITH AND WITHOUT 1kHz FILTER (Gain = 1152, Coarse Offset = 0mV) Noise Spectral Density (V/√Hz) 0.001 No Filter 0.0001 0.00001 1k Filter 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-5. Noise with 1kHz Filter, No Coarse Offset 10.0kS/s 20.0mV C1 RMS 8.92mV 5.00ms Figure A-6. Noise Measurement SBOA110A – June 2005 – Revised November 2005 Measurement Results 13 www.ti.com Appendix A PGA309 WITH AND WITHOUT 1kHz FILTER (Gain = 1152, Coarse Offset = 48mV) Noise Spectral Density (V/√Hz) 0.01 No Filter 0.001 0.0001 0.00001 1k Filter 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-7. Noise with 1kHz Filter, Maximum Coarse Offset 250kS/s 20.0mV C1 RMS 11.16mV 200µs Figure A-8. Noise Measurement 14 Measurement Results SBOA110A – June 2005 – Revised November 2005 www.ti.com Appendix A PGA309 WITH AND WITHOUT 1kHz FILTER (Gain = 1152, Coarse Offset = 0mV) Noise Spectral Density (V/√Hz) 0.001 No Filter 0.0001 0.00001 10k No Coarse 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-9. Noise with 10kHz Filter, No Coarse Offset 10.0kS/s 50.0mV C1 RMS 17.8mV 5.00ms Figure A-10. Noise Measurement SBOA110A – June 2005 – Revised November 2005 Measurement Results 15 www.ti.com Appendix A PGA309 WITH AND WITHOUT 10kHz FILTER (Gain = 1152, Coarse Offset = 48mV) Noise Spectral Density (V/√Hz) 0.01 No Filter 0.001 0.0001 0.00001 10k With Coarse 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-11. Noise with 10kHz Filter, Maximum Coarse Offset 250kS/s 50.0mV C1 RMS 42.1mV 200µs Figure A-12. Noise Measurement 16 Measurement Results SBOA110A – June 2005 – Revised November 2005 www.ti.com Appendix A PGA309 WITH MAX BANDWIDTH (Gain = 1152, Coarse Offset = 0mV) Noise Spectral Density (V/√Hz) 0.01 No Filter 0.001 0.0001 0.00001 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-13. Noise with Maximum Bandwidth, No Coarse Offset C1 RMS 26.3mV 50.0mV 5.00ms Figure A-14. Noise Measurement SBOA110A – June 2005 – Revised November 2005 Measurement Results 17 www.ti.com Appendix A PGA309 WITH MAX BANDWIDTH (Gain = 1152, Coarse Offset = 48mV) Noise Spectral Density (V/√Hz) 0.01 No Filter 0.001 0.0001 0.00001 0.000001 1 10 100 1k 10k Frequency (Hz) Figure A-15. Noise with Maximum Bandwidth, Maximum Coarse Offset 250kS/s 50.0mV C1 RMS 65.3mV 200µs Figure A-16. 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