Sailesh Chittipeddi - EEWeb

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<strong>EEWeb</strong> PULSE dbV@VOUT/dB 10 0 -10 -20 -30 -40 100 200 400 1k 2k 4k 10k 20k 40k 100k 200k 400k 1M 2M 4M 10M Frequency/Hertz Figure 11: Gain of 1, 2nd order SKF high pass frequency response. Output Noise / V/rtHz 10u 4u 2u 1u 400n 200n 100n 40n 20n 100 200 400 1k 2k 4k 10k 20k 40k 100k 200k 400k 1M 2M 4M 10M Frequency/Hertz Figure 12: Gain of 1, 2nd order SKF high pass output spot noise VIN / V 100k 40k 20k 10k 4k 2k 1k 400 200 100 200 400 1k 2k 4k 10k 20k 40k 100k 200k 400k 1M 2M 4M 10M Frequency/Hertz Figure 13: Input impedance to the design of Figure 10. intended signal frequency span causes the apparent input impedance to vary widely and extend to very low values as shown in Figure 13. This impedance looks roughly like a capacitance again above 20kHz. If this stage is then driven from the output of another amplifier stage, some impact on the response flatness of that device should be expected. Whether this V+ X1 Vin + ISL28136 – + – V– 33.3n C 1 33.3n C 2 1.25u R 2 20 Rb ISL28113 + + – – -9.29209u Figure 14: High Q, K=1 HPF driven by another amplifier stage. 457 R 1 50k 20 <strong>EEWeb</strong> | Electrical Engineering Community 10k R f V+ V– Vout impedance profile impacts the overall performance depends strongly on the specific device driving into this load. Using an ISL28136 (ref. 5) will give the circuit of Figure 14. This slightly lower noise device is faster and hence more susceptible to capacitive load peaking issues. This is shown as just a buffer stage here, but normally this would be another active filter stage to implement a multipole high pass filter. Running a frequency response and probing the output of the first stage (red curve) along with the final output gives the desired high pass complex pole filter shape but now adds perhaps an undesirable peaking at higher frequencies. dB 10 0 -10 -20 -30 -40 -50 100 200 400 1k 2k 4k 10k 20k 40k 100k 200k 400k 1M 2M 4M 10M Frequency/Hertz Figure 15: Buffered 2nd order SKF HPF response showing input impedance effects. This issue was showing up in the construction of an online semi-automatic multi-stage high pass active filter design tool. Many amplifier and impedance combinations are possible, but using a gain of 1 for the higher Q stages introduces a very wide component ratio spread that causes other problems as well. While increasing the gain for the highest Q stage seems like it is going in the wrong direction, it is actually possible numerous 2nd order benefits will be seen in physical implementations. Using K=2 in the SKF HPF to improve the input impedance characteristic. The parametric R vs. C ratio curves shows a significant reduction in required R ratio with that addition of some gain in the amplifier. Then, starting from an R2 value that does not impact the total noise too much, using a K=2 will pull up the required R1 value nicely. Continuing with the equal C design for simplicity and holding R2 = 50kΩ adjusts the C values down and the R1 value up for 1kHz, Q = 5.27 design as shown in figure 9. With R1 resolved to 28.6kΩ using eq. 4, the R1C product will be given by eq. 5 for k>1 (letting k=1 gives the solution for the C in the first example). Dividing this result by R1, gives the value for the equal C in this design flow.
Vin R1C = 1 1+ 4ω0Q 1+8Q2 (k − 1) 4.2n C 1 4.2n C 2 1.25u 28.6k R 2 R 1 20 Rb ISL28113 + + – – -18.8333u Figure 17: K=2 design for Fo = 1kHz, Q = 5.23, low power HPF using the ISL28113. 50k The response shows the same high pass poles as the unity gain design (shifted up 6dB) but of course lower high end cutoff frequency. The frequency response for the unity gain design and this K=2 design are shown in Figure 18. These responses are not following a strict gain bandwidth product profile due the correctly modeled open loop phase effects in the ISL28113 macromodel. It is not uncommon to see a bit of bandwidth extension in VFA based designs operating at lower gains where the phase margin is
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