# Signal Chain Basics #133: Designing summing active filters

In this article, I’ll describe a few easy steps that will convert any Sallen-Key (SK) or multiple feedback (MFB) active filter from a single-input filter to a summing active filter that gives the same response without difficult calculations or analysis.

First, let’s review the basic inverting summing amplifier shown in Figure 1. Adding the feedback capacitor in parallel with the feedback resistor results in a first-order low-pass filter response. This circuit can accept any number of inputs that will be summed together, gained and low-pass-filtered, as shown in the transfer function shown in Equation 1: Figure 1 Inverting summing amplifier with G = -10V/V and first-order low-pass filter

You can apply the same concepts of the summing amplifier to active filters to sum multiple signals together while applying the desired active filter response. Figure 2 shows an MFB low-pass filter with a cutoff frequency of 1kHz and a Butterworth response. The values for the components were determined using the Texas Instruments filter designer tool.

Figure 2 MFB active low-pass filter with 1kHz cutoff frequency and Butterworth response

The circuit in Figure 2 is traditionally designed to accept one input signal, but you can easily modify it to accept two or more inputs without affecting the cutoff frequency (-3dB frequency). First, add a second input resistor (R4) in parallel with R1. The parallel combination of these two resistors must match the original value of R1 so as not to affect the filter frequency response. Since resistors add reciprocally in parallel, both resistor values need to be doubled from 8.25k to 16.5k. These changes result in both inputs having the same -3dB cutoff frequency as the original filter. However, both inputs will be attenuated by 0.5V/V (-6.02dB) due to the resistor divider formed between R1, R4 and the other input signal. Figure 3 shows the circuit and results.

Figure 3 A modified MFB low-pass filter sums two inputs together with the same 1kHz cutoff frequency

To achieve the original unity-gain (0dB) response, start by using the filter designer software to design the filter for a gain of 2V/V (6.02dB) with the same 1kHz cutoff frequency. Perform the same steps listed above to add the second input while maintaining the same cutoff frequency. Now the -6.02dB attenuation is corrected by the 6.02dB gain of the active filter; the result is that both inputs are summed together with a unity-gain response and filtered at the desired 1kHz cutoff frequency. Figure 4 shows the results.

Figure 4 Modifying a 2V/V MFB low-pass filter to a unity-gain two-input summing filter with AC results

Figure 5 shows the transient results for this circuit with 1Vpp sine and cosine 100Hz inputs for Vin1 and Vin2. The two 90-degree out-of-phase 1Vpp input signals sum together to produce the 1.414Vpp output waveform.

Figure 5 Transient response of the summing active low-pass filter

You can apply the same concept for additional inputs by starting with a gain equal to the number of inputs and then adjusting the input component accordingly. A three-input MFB low-pass filter starts with a gain of 3V/V filter design and then increases each input resistor to three times the original value. Figure 6 shows the original 3V/V filter and the modified circuit to accept three inputs with AC.

Figure 6 Modifying a 3V/V MFB low-pass filter to a unity-gain three-input summing filter with AC results

You can modify MFB high-pass and band-pass filters (as well as the same Sallen Key {SK} filters) to sum multiple inputs using the same method. High-pass filters have capacitors as the input components, unlike the low-pass and band-pass filter topologies. Since capacitors add in parallel, the input capacitor values need to be divided by the number of stages.

Figure 7 shows a 2V/V gain 1kHz SK high-pass filter with a Butterworth response and the two-input summing active filter with the same response that was created from it.

Figure 7 Modifying a 2V/V SK high-pass filter to a unity-gain two-input summing filter with AC results

You can modify active filter circuits to sum multiple inputs together by following the simple steps described in this article. Start by designing an active filter with a gain equal to the number of inputs that will be summed together. If the input component is a resistor, the values will need to be increased such that the parallel combination is equal to the original value. Input capacitors need to be decreased such that their parallel combination adds to the original value. This method works best when summing up to five inputs; otherwise the required active filter gain starts to get too high, causing stability concerns. To learn more about summing amplifiers, download the Analog Engineer’s Pocket Reference and the Handbook of Operational Amplifier Applications.

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## 1 comment on “Signal Chain Basics #133: Designing summing active filters”

1. gufo
March 1, 2018

Easy to follow design-procedure. Thanks for sharing, Collin. To your experience, what would be the top three use cases for a summing inverting filter?

/Gustaf

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