Tutorial 3 - Frequency Response of Filters Part 2

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38:23

• Calculating gain
• Calculating phase
• Calculating output change when changing frequency

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04:33 Frequency Response

• Magnitude vs. $\omega$
  • put all $s$ in $H(s)$ into $\frac{s}{\omega }+1$
  • magnitude = $20\log \text{(number mutliplied by s)}$
  • Bode Plot: Go up/down at each frequency of $s$
    • Upper $s$ (zeros) → up | Lower $s$ (poles) → down
    • Up/down by 20dB/dec
    • Up/down at $\omega =$ number below $s$ in $s+1$
    • Free $s$ with no $s+1$ means up/down at $\omega =0$
  • 3dB Roll Off Frequency ⇒ magnitude - 3dB
• Phase vs. $\omega$
  • $\theta =\arctan \left(\frac{\text{img}}{\text{real}}\right)$
  • $\angle H(s)=\angle {\theta }_{\text{numerator}}-\angle {\theta }_{\text{denominator}}$
  • Substitute at each ${\omega }_i$ with $\omega$ >>> ${\omega }_i$ and $\omega$ <<< ${\omega }_i$
• Deduce type of filter from the response

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08:35 Problem 2 - Sheet 2

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26:26 Problem 3

• Derive transfer function

  • Resistance of C is $\frac{1}{sc}$

  • Use nodal analysis

  • Use known Op-Amp Circuits

$R_{in}$ does not include reactance, only resistances

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55:53 3dB Roll Off Frequency

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