Frequency Response

Frequency Response

1. Gain Response

   • Bandwidth
     • BW = f(H) - f(L)
       • diff between high power frequencies
     • find A(max)
       • use eqn to find A
         • read off graph

2. Bode-gain plot

   • gain vs log(f)
     • 20log(A) vs log(f)
   • measures
     • frequencies
       • decade
         • f(2) = 10 f(1)
       • octave
         • f(2) = 2 f(1)
     • gain
       • decibels (dB)
         • A(dB)
           • 20log(A)
   • f(H) & f(L)
     • @ A(dB) = A(dBmax) - 3dB

3. Low frequency response

   • capacitor reactance, X(c)
     • 1 / 2πfC
       • = 1 / ωC
     • decreases as f increases

4. f = 1 / 2πRC

5. Low pass filter

   • passive
     • 1st order
       • roll-off of 20dB/dec
         • max gain
           • = 1
   • active
     • low frequency
       • "open circuit"
         • R no effect on gain
     • BW & cut-off frequency
       • still determined by R & C
     • 20dB/dec roll-off

6. AC

   • capacitor
     • high frequency
       • low impedance
         • "short circuit"
           • V(o) = V(i)
             • A = 1
     • low frequency
       • high impedance
         • "open circuit"
           • V(o) = 0

7. High pass filter

   • active
     • 1st order
       • low freq
         • "open"
           • zero output
       • high freq
         • "short"
           • acts as basic non-inverting amp

8. Band-Pass filter

   • connecting high-pass to low-pass
   • center freq
     • f = √ [f(H)f(L)]
   • Q parameter
     • high-Q band pass
       • f(H)
       • f(L)
     • measure of selectivity
     • f / BW

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