Derivative-controlled low pass filter, simplified

How to design a simpler filter (or filter-like circuit) with a varying time constant dependent on what kind of waveform is fed to it.

Discussions with some former coworkers have focused on how to design a filter or circuit with filter-like performance that has the characteristic of a slower time constant on on increasing-signal waveforms and a faster time constant on decreasing-signal ones. Such a circuit was proposed in Reference 1, which made use of the Analog Devices AD534 chip.

Wow the engineering world with your unique design: Design Ideas Submission Guide

Along with the “squirming baby” example in Reference 1, another example using such a filter might be a scale at a deli counter, filtering weight as a slice or two is added to the order. When weighing is complete and the slices are removed from the scale, the reading should conversely decrease quickly.

Could there be a different, simplified circuit that might find use in accomplishing the same effect? Thus this Design Idea.

Simplification using an op amp

One way to simplify is to use the same input voltage level as the output, which precludes requiring an input isolation circuit. See Figure 1 for an example.

Figure 1 This simplified derivative-controlled low pass filter has its output at V.

Starting with the circuit in Reference 1 as a foundation, the simplified circuit requires an R₁C₂ combination to act as the derivative function. The input signal requires a filter, R₃C₁ as the filter time constant. This derivative signal should be wired to a transistor switch, Q₁, a 2N2907A, which discharges that capacitor at a faster rate, R₄C₁. A non inverting amplifier, ¼ of an LM324N, acts to provide isolation of the derivative input to the transistor switch. This is accomplished by ensuring that the Q₁ emitter to base junction is zero, therefore not conducting at steady state.

Figures 2-4 show the actual circuit being tested, and the results.

Figure 2 The circuit in this Design Idea was breadboarded and lab-tested, not just simulated.

Figure 3 In this graph of test results, the red trace is the input, with the output at C₁ in blue. Note that the output is at the same level as the input, but the time constants are different.

Figure 4 Conversely, in this graph of test results, the red trace is the output and the blue trace shows the derivative action.

Further simplification

Removing the op amp is possible if the emitter to base junction is biased below the cut-in voltage. Reference 2 has an extensive discussion on the subject, based on the Shockley diode equation. The emitter base junction is the diode in question. There is a point where the forward bias current quite low, assumed to be 1% of the maximum load current. The voltage at that point is considered to be the cut-in voltage; for silicon devices it is assumed to be 0.6V.

For this application, R₁ is lowered to 500Ω, which results in a 0.238V difference across the forward-biased Q₁ junction, below the cut-in voltage at steady state.

Figure 5 This schematic shows a further simplification of the previous circuit.

Figure 6 In this graph of test results for the further simplified version of the circuit, the red trace is again the input, with the output at C₁ in blue.

Figure 7 Conversely, in this graph of test results for the further simplified version of the circuit, the red trace shows the voltage across R₁, with the blue trace referencing the C₁ voltage. Note the voltage difference in this case.

Conclusion

This circuit will not work for small changes in the input voltage, a topic which is discussed in Reference 1. The values used in these circuits are arbitrary; they can be scaled based on filtering requirements.

References

1. Sheingold, Daniel H., Transducer Interfacing Handbook, Analog Devices, Inc., Norwood, MA., 1980.
2. Millman, J.; Taub, H., Pulse, Digital, and Switching Waveforms, McGraw-Hill, New York, NY., 1965.

Robert Heider is a retired engineer with over 50 years’ experience with emphasis on the design of advanced process controls and process development.

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