This circuit is a two-pole, active lowpass filter with zero offset.

This circuit is a two-pole, active lowpass filter. The DC path from input E1 to output Eo is via R1 alone and does not involve the op amp. Because C1 and C2 are DC blocks from the op amp to the signal path, there is zero DC offset effect coming from the op amp.

**Figure 1** Zero offset active lowpass filter

The algebraic derivation of the transfer function of this circuit is the following:

**Figure 2** Transfer function derivation, part 1

**Figure 3** Transfer function derivation, part 2

If we arbitrarily set R1 = R2 = 10K and C1 = C2 = 0.01 µF and then use this derived transfer function, we calculate the following response.

**Figure 4** Algebraically derived frequency response

The algebraic frequency response result is replicated in the following MultiSim SPICE model:

**Figure 5** SPICE model of two pole filter frequency response

One nice thing about this circuit is that you can cascade two or more of them to make higher order lowpass filters. Although trying to work out the applicable algebra for the higher order filters lies beyond my patience threshold, SPICE simulations can be revealing.

**Figure 6** SPICE model of six pole frequency response

All of the op amps are DC blocked from the signal path. Only resistors are found in the signal path and they do not induce DC offsets.

However, please bear in mind that each section does indeed load the previous section and therefore, the sections' individual transfer functions interact. The loading effects are significant. Fortunately, it's easy to make and use SPICE models. With some judicious component value adjustments, useful results are easily obtained.

**Editor’s note**: Please say a prayer for John, he is in the hospital with some medical issues. He is a long-time friend of mine and has been writing this Living Analog blog series since 2012. John and I were both on the IEEE Executive Committee on Long Island, NY.

—Steve Taranovich

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