Simulation Results

All circuits were simulated using KiCad.

Frequency Response

Filter Behavior

Our Butterworth filters exhibited different behavior at varying gains. At a gain of 2, the 2-pole high pass filter exhibited resonance, with a noticeable peak near the cutoff frequency. As we further increased the gain, we observed a shift in the cutoff frequency. To maintain optimal filter performance, we concluded that it was necessary to implement a second gain stage after the low-pass and high-pass filters.

Gain = 1

Gain = 5

Gain = 2

Gain = 100

Frequency Response after Each Stage

Va: after the first gain stage
Vb: after the 4-pole low-pass filter
Vc: after the 2-pole low-pass filter
Vout: the final output

Transient Analysis

Sinusoidal Input

Vin+: 1 uV, 1k Hz, 0 DC offset
Vin-: -1 uV, 1k Hz, 0 DC offset

Va: Some DC offset is introduced by the differential amplifier.

Vc & Vd: More DC offset is introduced by the 4-pole lowpass filter (Vc), which is removed by the 2-pole highpass filter (Vd).

Vout: The final output is amplified and exhibits little DC offset.

Sinusoidal Input with White Noise

Vin+: 1 uV, 1k Hz, 0 DC offset, white noise with 100 nV RMS
Vin-: -1 uV, 1k Hz, 0 DC offset, white noise with 100 nV RMS

Sinusoidal Input with 60 Hz Noise

Vin+: 1 uV, 1k Hz, 0 DC offset, 10 uV 60 Hz noise
Vin-: -1 uV, 1k Hz, 0 DC offset,10 uV 60 Hz noise

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