Two-stage pass-band filter - Overall gain

[JJBladester]

Homework Statement

When calculating the overall gain of a two-stage pass-band filter, can one simply add the gain from the high-pass filter (R1/C1) to the gain from the low-pass filter (R2/C2)?

Homework Equations

N/A.

The Attempt at a Solution

For example, if the gain from the high-pass filter was -2dB and the gain from the low-pass filter was -5dB, is the overall gain -7dB?

My book does not go into an explanation on how this works. I may just set up a test circuit in MultiSim to get a general idea of the output gain w.r.t. the individual gains of the high- and low-pass filters.

 

[gneill]

In general, no, as the input impedance of the second stage will affect the first stage's response, while the output impedance of the first stage affects the second's.

However, if components are selected carefully to minimize the loading, then adding the gains will give a good approximation. For example, make the input impedance of the second stage about 10x that of the output impedance of the first stage.

 

[NascentOxygen]

When calculating the overall gain of a two-stage pass-band filter, can one simply add the gain from the high-pass filter (R1/C1) to the gain from the low-pass filter (R2/C2)?

See https://www.physicsforums.com/showthread.php?t=652403

 

[JJBladester]

See https://www.physicsforums.com/showthread.php?t=652403

NascentOxygen,

Thank you... This other thread was extremely helpful.

 

[rezeew]

I would like to clarify that the overall gain of a two-stage pass-band filter cannot simply be calculated by adding the individual gains of the high-pass and low-pass filters. This is because the two stages of the filter interact with each other and affect the overall output gain.

To accurately calculate the overall gain, you will need to consider the transfer function of the entire filter, which takes into account the frequency response of each stage and their combined effect. The transfer function can be derived using circuit analysis techniques or by using software such as MultiSim.

Furthermore, the overall gain of a two-stage pass-band filter can also be affected by the component values (R1, R2, C1, C2) and the order in which the stages are connected. Therefore, it is important to carefully design the filter and consider all these factors in order to achieve the desired overall gain.

In summary, the overall gain of a two-stage pass-band filter cannot be simply calculated by adding the individual gains of the high-pass and low-pass filters. It is a complex system and requires careful analysis and design to determine the accurate overall gain.