# How to design Twin-T Bandpass Filter

One of the popular circuit topology for filter design is the twin-t filter topology. This filter topology is mostly used to design twin t notch filter but can also be employed to design Twin-T Low Pass Filters (LPF), Twin-T How Pass Filters (HPF) and Twin-T Bandpass Filter. Actually we can also utilize the twin-t configuration to design twin t oscillator. This versatile circuit configuration allows for the creation of filters that selectively pass or reject certain frequencies. By adjusting the component values in the twin-T network, one can tailor the filter's behavior to suit either high pas, low pass and bandpass filtering requirements. The twin-T topology also offers flexibility in designing filters across various frequency ranges. Here we will consider the design and circuit operation of Twin-T topology based Bandpass Filter.

### Twin-T Bandpass Filter Circuit Diagram

Below is the circuit diagram of a twin-t bandpass filter.

Here the two R resistors of equal values and 2C forms one T section and the C of equal value and R/2 forms the second T section. Each of the section performs low pass filtering and high pass filtering and the lower to the higher frequency cutoff is the bandwidth of the band pass filter.

#### Twin-T Bandpass Filter Design Example

Here is a circuit of bandpass filter using twin-t configuration with LM358 operational amplifier.

The value of the filter components were calculated for center frequency of 1KHz,

The center frequency of the the twin-t bandpass filter is given by,

$f_{c}= \frac{1}{2 \pi R C }$

The lower and upper cutoff frequencies of the bandpass filter can be calculated using the following equation.

$f_{c}= \sqrt{f_L f_H }$

If we choose C=0.047uF and since center frequency fc=1KHz, the value of R is 3.4KOhm.

The following shows the frequency response of this twin-t bandpass filter.

Consider that we fed into this twin-t filter a 5KHz signal with 200mV amplitude. Then we can observe using frequency spectrum that the filter indeed suppresses the signal at 5KHz.

#### Disadvantages and shortcoming of Twin-T Bandpass filter

Twin-T Bandpass filter is not a true bandpass topology. It is more of a resonator with a sharp peak. In an ideal setup, this configuration boasts infinite gain at its resonance. However, practical application grapples with gain control precisely at the central frequency, resulting in a stop band rejection of 0 dB, equating to unity gain. Consequently, its effectiveness in rejecting signals outside the desired band is limited in real-world scenarios.

Furthermore working with this configuration presents significant challenges. It necessitates acquiring three resistors, where one is precisely half the value of another, and three capacitors, with one being precisely double the value of another. Even if one manages to find such components, the likelihood of an exact match or consistent performance across temperature variations is slim. Additionally, the sharpness of the peak might lead to real-world components either degrading the peak or completely bypassing it.

### Adjustable Q and BW Twin-T Bandpass Filter Design

In the simple Twin-T Bandpass Filter design above, the frequency response is sharp and Q is too high for actual bandpass filter application. But it is possible to get wider frequency response with a modified Twin-T Bandpass Filter topology as shown below.

This setup optimizes the utilization of parallel resistance and capacitance traits to simplify your tasks. Introducing R and C as additions reduces the search to just four matching resistance and capacitance values each, eliminating the need for 2C and 1/2R. Given components from the same production batch tend to exhibit nearly identical traits, this becomes a straightforward process.

An intriguing alteration to the familiar Twin-T topology involves the incorporation of Ra and R. These elements capitalize on the only two points in the circuit where the Q can be adjusted. While ensuring Ra remains close to R, it minimally impacts the central frequency but alters the appearance of the two series C, inducing a reduction in peak amplitude. Similarly, with Rb significantly less than R, it alters the parallel C, creating a higher equivalent series resistance (ESR), thereby diminishing the peak. Although their combined effect grants a degree of control over amplitude and peak, it might not meet the precision levels expected. Upon comparing the modified and unmodified circuits' responses, the tendency for amplitude to spiral at resonance has been curbed, rendering a more rational response. The adjustment also affects the Q, albeit challenging to discern on the logarithmic frequency scale spanning four decades.

#### Design example

Below is one example design of modified twin-t bandpass filter:

The frequency response of modified twin-t bandpass filter designed above is shown below.

Clearly there is improvement in the sharpness of the frequency response and wider bandwidth.