EDN Access -- 03.02.95 Notch filter is dc accurat
Design Ideas:March 2, 1995
Notch filter is dc accurate
Maxim Integrated Products, Sunnyvale, CA
Most active filters exhibit noise, distortion, gain error, and dc offset. However, a filter topology that separates the dc and ac paths can eliminate the last two of these unwanted behaviors (Fig 1a). The dc path in this circuit has no op amps and, therefore, no dc offset. The dc path does not have a dc gain error other than -6 dB of attenuation that the R1/R2 divider causes. (This attenuation is absent if you omit the R2 termination.) The ac path consists of C1 and a synthetic inductor comprising two wideband transconductance amplifiers and associated components. The result is an active circuit that emulates the passive filter of Fig 1b.
Simulating the inductance avoids the use of an actual inductor, which can act as a transmitting and receiving antenna for EMI. The equivalent inductance LEQ equals C2/(gm1xgm2, where gm1 and gm2 are the transconductances produced by IC1 and IC2. The inductance value can be large if gm1xgm2 is much less than 1, but one end of the network must always connect to ground. Each gm is set by an external resistor (R3 and R4 for IC1 and IC2, respectively) according to the relationship gm=8/R.
For optimum noise performance, the gm values should allow a full range of output swing for each amplifier. Starting with equal gm values, simulate the filter in Spice using "g" elements for the amplifiers. Observe the peak voltage at each amplifier's output while sweeping the frequency at least one decade above and below the filter's corner frequency (in this case, 3.2 kHz.)
The overall filter determines the peak voltage across the synthesized inductor at pin 13 of IC2. Therefore, you adjust the peak value at IC1's pin 13 to match that of IC2 by varying the gms. Let K equal the ratio of these peak values, which are VO1(PK)/VO2(PK). Gain is proportional to transconductance, so divide gm1 by K and multiply gm2 by K. Then, rerun Spice with the new gm values to verify that the peaks are equal and the filter shape hasn't changed.
Testing of the entire filter—the source/load connection shunted by the series network of C1 and the synthetic inductor—on a network analyzer that includes the 50 Ohms R1 and R2 resistors shows a second-order notch response. The rejection at the 3.2-kHz corner frequency is about 40 dB. The parasitic capacitance between the synthetic inductor's output and ground is the main contributor to high-frequency error. This error, though small, increases as the parasitic reactance approaches the parallel combination of the R1 and R2 source and load resistances. To minimize error in the frequency response, you should keep these resistances small with respect to the amplifiers' 3-kOhm output impedances.EDN Magazine. EDN is a registered trademark of Reed Properties Inc, used under license.