One of the popular circuit topologies for filter design is the twin-T filter topology. This filter topology is mostly used to design twin T notch filters but can also be employed to design Twin-T Low Pass Filters (LPF), Twin-T High Pass Filters (HPF), and Twin-T Bandpass Filters. Actually, we can also utilize the twin-T configuration to design a 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 high pass, 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 a 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 form one T-section, and the capacitor C and R/2 form the second T-section. Each section performs low pass filtering and high pass filtering; the range from the lower to the higher frequency cutoff constitutes the bandwidth of the bandpass filter.
Twin-T Bandpass Filter Design Example
Here is a circuit of a bandpass filter using a twin-T configuration with the LM358 operational amplifier.
The values of the filter components were calculated for a center frequency of 1kHz. The center frequency ($f_c$) of 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 = 0.047µF and a center frequency $f_c$ = 1kHz, the value of R is approximately 3.4k$\Omega$.
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. We can observe using a frequency spectrum that the filter indeed suppresses the signal at 5kHz.
Disadvantages and Shortcomings of Twin-T Bandpass Filter
The Twin-T Bandpass filter is not a "true" bandpass topology in the traditional sense; 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, often resulting in a stopband rejection of 0 dB (unity gain). Consequently, its effectiveness in rejecting signals far outside the desired band is limited in real-world scenarios.
Furthermore, working with this configuration presents challenges. It necessitates acquiring three resistors where one is precisely half the value of another, and three capacitors where one is precisely double the value of another. Even with these components, the likelihood of an exact match or consistent performance across temperature variations is slim. The extreme sharpness of the peak means that real-world component tolerances might either degrade the peak or miss it entirely.
Adjustable Q and BW Twin-T Bandpass Filter Design
In the simple Twin-T design above, the response is often too sharp for general bandpass applications. However, it is possible to achieve a wider frequency response with a modified Twin-T Bandpass Filter topology as shown below.
This setup simplifies the task by using parallel resistances and capacitances. Introducing $R_a$ and $R_b$ allows for Q adjustment. By matching four identical resistors and capacitors (eliminating the need for exact 2C and 1/2R values), the process becomes much more straightforward using components from the same production batch.
The incorporation of $R_a$ and $R_b$ targets the points in the circuit where Q can be tuned. When $R_a$ remains close to R, it minimally impacts the center frequency but reduces peak amplitude. Similarly, making $R_b$ significantly less than R creates a higher equivalent series resistance (ESR), diminishing the peak. Comparing the modified and unmodified responses, the tendency for amplitude to spiral at resonance is curbed, rendering a more stable response.
Design Example
Below is an example design of a modified twin-T bandpass filter using the LM358:
The frequency response of the modified twin-T bandpass filter designed above is shown below:
Clearly, there is improvement in the stability of the frequency response and a more usable bandwidth for bandpass applications.
