Final answer:
To design a bandpass filter with two Thomas circuits and a mid-band gain of 1, the components within the circuits need to be selected to resonate at the desired frequency and give a resulting gain of unity.
Step-by-step explanation:
In designing a bandpass filter with two Thomas circuits, achieving a mid-band gain (H) of 1 requires setting the gain of both circuits to unity (1), or in other words, ensuring that the output voltage is equal to the input voltage at the mid-band frequency. The Thomas circuit typically includes a configuration of resistors, capacitors, and sometimes inductors to create a frequency-selective filter. The design parameters must be chosen such that they resonate at the desired mid-band frequency and combine to give the overall required gain.
To attain a mid-band gain of 1 in both Thomas circuits, the components within the circuits must be carefully selected and/or adjusted. This usually involves calculating the required values of capacitors and inductors based on desired resonant frequencies and other system characteristics such as impedance. It might also need iterative tuning to obtain the precise filter characteristics.