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Bandpass Filter. Approximate and Exact Solutions. The Circuit. Low-Pass Section R1 = 1k C1 = 10 nF High-Pass Section R2 = 100k C2 = 10 nF. Results for Ideal Cascade. Decibel gain. Phase shift. Transfer function: Ideal Cascade. Results for Exact Solution. Decibel gain. Phase shift.

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bandpass filter

Bandpass Filter

Approximate and Exact Solutions

the circuit
The Circuit

Low-Pass Section

R1 = 1k

C1 = 10 nF

High-Pass Section

R2 = 100k

C2 = 10 nF

results for ideal cascade
Results for Ideal Cascade

Decibel gain

Phase shift

results for exact solution
Results for Exact Solution

Decibel gain

Phase shift

comparison of solutions
Comparison of Solutions

Drum Roll Please…

is it always that easy
Is it always that easy?

Yes, it can be!

But design carefully!!

now modify the circuit
Now modify the circuit

Low-Pass Section

R1 = 1k

C1 = 10 nF

High-Pass Section

R2 = 100k/100 = 1k

C2 = 10*100 nF = 1uF

High pass modified

comparison of solutions1
Comparison of Solutions

Drum Roll Please…

boo big loss of signal that is supposed to pass
Boo—big loss of signal that is supposed to pass!

Blue = approximated solution, assuming “ideal” behavior

Red = exact/actual solution