**The Problem**

This converter, and the low-pass filter networks to make it work,
evolved out of our need for a precision rectifier to meet the
following performance requirements.

1) Good voltage conversion linearity over a 70 dB dynamic range,

2) Low output ripple at a minimum input frequency of 1 Hz,

3) A minimum output tracking delay, that is, an acceptable step
response, and

4) A flat frequency response from 1 Hz to 100 kHz.

As we might expect, there is some interdependence between these requirements. For example, the dynamic range is limited at the low- level end by the residual ripple and noise. The output ripple also causes a problem when we try to specify the low frequency end of the frequency response. In other words, 1 volt RMS at, say 1 Hz, should convert to 1 volt DC with only a small ripple content for us to say the response is "flat" down to 1 Hz.

**The Basic Circuit**

Figure 1 shows a basic precision rectifier which has been frequently described in the literature (e.g. references 1 and 2).

This seemed a good starting point so we built this circuit using Zeltex model 148 chopper-stabilized operational amplifiers. We picked these amplifiers for their high open-loop gain, low DC offset and excellent temperature and time stability specifications, but we expect there are other amplifiers on the market which would work as well.

We set Rf (Fig. 1) at 22.1 kohms to give a unity RMS to DC conversion factor for a sinusoidal input and as a starting point we chose C = 10 uF. We then measured the conversion dynamic range at a frequency of 1 kHz and found good linearity from 10 volts down to 3 millivolts - a range of slightly more than 70 dB. Repeated measurements at 100 Hz and 10 kHz gave essentially the same curve which is graphed in Figure 2.

Even at 100 Hz the output ripple was sufficiently low with C = 10uF. Indeed, the measuring process enhanced the filtering because we used an integrating digital voltmeter at the converter output.

We next ran a frequency response measurement at an input level of 3 volts RMS. We found the response down by about 0.5 dB at 100 kHz, as shown in Figure 3, which we felt was acceptable. This measurement didn't go below 100 Hz because it was obvious that the ripple amplitude became too large to yield meaningful results.

The circuit was built with 1N914 diodes but having a curious nature I substituted general purpose silicon diodes, type 1N456, and ran the response again. This result is also graphed in Figure 3 and speaks for itself. We also tried hot-carrier diodes, type HPA-2900, but found their performance indistinguishable from that of the 1N914's. The remainder of the measurements were made using the original diodes.

We already knew, of course, that the output ripple was large at low frequencies but such knowledge is not very quantitative so we measured the ripple at a constant input of 3 volts RMS. The curve labeled "Circuit 1, C = 10uF" in Figure 4 presents the results of this measurement.

(Incidentally, all voltage measurements below 10 Hz were made with a Ballantine model 316 Infrasonic peak-to-peak voltmeter and the readings converted to RMS by dividing by 2.83.)

Well, it's evident that output-ripple wise this circuit just doesn't do the job, so we changed C to 100 uF. Looking at the appropriate curve in Figure 4 we see that the output ripple was lowered by a factor of 10, as theory suggests it should be.

Recalling that a capacitor in parallel with an op-amp's feedback resistor is really just a one-pole low-pass filter we would further expect the two "Circuit 1" curves, in Figure 4, to have slopes of 6 dB/octave or 20 dB/decade, which they do. I, for one, am always pleased (and faintly surprised) when measurements agree so well with theory.

We still have the problem of measuring the converter's response time, or settling time or more correctly its step response. To make this measurement we set up the circuit diagrammed in Figure 5 and applied, as a step, a 3 volt RMS sinusoid with a frequency of 1 Hz.

Using the same labels as before we have graphed these measurements in Figure 6. As we might have expected, "Circuit 1, C = 100uF" is pretty sluggish - so back to the drawing board.

**Improved Filter**

The intuitive solution to our problem of keeping the ripple low while at the same time minimizing settling time is to use a fancier output filter.

Well, at the frequencies involved a passive filter would physically be a beast - which leaves active filters. But to avoid losing the benefits of having used chopper-stabilized amplifiers in the basic converter we need an active filter with comparable DC offset and stability.

So now we finally get to the commercial. We can easily make such a filter using one of our MA-series networks and another chopper- stabilized op-amp. Since we need a predictable step response, a fairly steep rolloff rate and unity DC gain a Butterworth response seemed a good choice. And because the design equations are easier to handle we decided on a 3-pole network. Also using the constraint of requiring the network to fit into our standard size "A" module (2 x 1.125 x .625 inches), George (that's what we call our digital computer) told us the minimum cutoff frequency was 2.5 Hz assuming an input impedance of 100 kohms.

Even though it was clear that this circuit would be even worse that "Circuit 1, C = 10uF" at low frequencies, we built the network to verify the design. The converter circuit is shown in Figure 7 and the measured output ripple is the curve labeled "Circuit 2, fc = 2.5 Hz" in Figure 4.

Note that since the active filter is inverting, the converter diodes were reversed in direction to preserve the positive-going output.

Well then, let's take one more step and lower the cutoff frequency by a factor of 10, this time with the requirement that the network fit our size "B-1" module (2.4 x 1.5 x .625 inches). George came up with the design partially given in Figure 8 using two positive impedance converters (PIC's) as capacitance multipliers.

This is still a passive network even though it now requires a +/-15 volt DC power supply to operate the PIC's. By proper design the external op-amp thinks the network is indeed passive and the DC offset and stability still meet the original op-amp specs.

Figure 9 is a photograph of the basic converter and the 3-pole Butterworth filter (fc = 0.25 Hz) breadboard. The ripple and step response are presented in their respective figures and we can see that we now have an output ripple at 1 Hz a bit lower than "Circuit 1, C = 100uF" and a much faster settling time.

**Conclusion**

Whether this final circuit (Fig. 7) meets our design objectives depends on how we define good, minimum and acceptable in the Problem statement on page 1. In any event, it proved to be good enough for our present need. Perhaps the most important aspect of this exercise has been our rather exact determination of the performance limitations of the circuits we looked at.

The Butterworth step response overshoot may be troublesome in some cases. Should this happen we can build and plug-in a Bessel response network. The price paid, of course, is that for the same number of poles we will have a longer settling time and a less steep rolloff rate.

**References**

1. "Handbook of Operational Amplifier Applications", Burr-Brown Research Corp., Tuscon, Arizona. 1963.

2. "Applications Manual for Computing Amplifiers", Philbrick Researches, Inc., (now Philbrick/Nexus) Dedham, Massachusetts. 1966.

**An Update Appendix, added March 1998**

Zeltex, Inc. the manufacturer of the chopper-stabilized opamps used in this Note no longer exists. Integrated circuit chopper-stabilized opamps did not exist in 1970 but they do now, and probably with better specs. But it may be that present-day non chopper-stabilized opamps will meet the DC offset, temperature and time stability requirements.

We have not built MA-series networks for some years as there are now better and smaller ways to make active filters.

The positive impedance converter is still a good way to build a lowpass filter with a low cutoff frequency. See any modern filter design text for details.

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