High Q value filter circuit graphic analysis

1) There is a circuit on the network that achieves a high-bandwidth bandpass filtering effect by using a high R3/Req ratio. However, due to the GBW (Gain Bandwidth Product) limitation of the operational amplifier, the actual center frequency of the circuit ends up being lower than the theoretical value calculated. This is an important consideration when designing such filters for high-frequency applications.

2) Regarding the resistance and notch filter design, there are many complex 50Hz notch circuits available online. After performing multiple simulations and analyses, I derived a simple formula for creating notches at any desired frequency: fn = 1 / (2πC√(R2R)). By fine-tuning resistor R2, the output waveform can be perfectly aligned with the input. Then, by inverting the signal and adjusting it to zero using R3, the best notch performance is achieved.

Based on the original circuit parameters, the notch frequency is calculated as fn = 1 / [2π(0.1×10⁻⁶)√(411×10³ × 2.4×10³)] = 50Hz.

If the capacitance is changed to C = 2μF while keeping other components unchanged, the new notch frequency becomes fn = 1 / [2π(2×10⁻⁶)(√(411×2.4)×10³)] = 2.5Hz.

Although the GBW parameter of the op-amp has minimal impact on the notch frequency itself, it does introduce a low-pass filtering effect on signals above the GBW limit, which should be taken into account when working with higher frequencies.

3) For bandpass filtering using resistance, the previously mentioned band-stop circuit operates differentially. The time constant at the negative terminal determines the passband of the circuit. When a sine wave at the notch frequency (fn) is applied, if R1:R3 equals Re:Rf (where Re and Rf represent equivalent resistances for the respective frequencies), the differential output will be zero, effectively canceling out the fn frequency. When R3 is adjusted appropriately, this creates a more pronounced notch effect.

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