13/08/26 Thu 8:05am

Number of poles and zeros stay the same

TF = \frac{s - α}{s + α}

Step 1: $V_{2} = 0, V_{i} remains as it is$

V_{01} = \frac{R}{R} V_{1} = - V_{i}

step 2: $V_{1} = 0$ & $V_{2}$ remain as it is at this $V_{0} = V_{02}$

V_{A} = \frac{V _{i} \times \frac{1}{SC}}{\frac{1}{SC} + R} = \frac{V _{i}}{SCR + 1}

V_{02} = (1 + \frac{R _{f}}{R _{in}}) . V_{A}

V_{02} = 2. \frac{V _{i}}{SCR + 1}

V_{0} = V_{01} + V_{02}

V_{0} = - V_{i} + \frac{2 V _{i}}{SCR + 1}

V_{0} = V_{i} \frac{- SCR - 1 + 2}{1 + SCR}

V_{0} = V_{i} \frac{1 - SCR}{1 + SCR}

TF = \frac{V _{0}}{V _{i}} = \frac{1 - SCR}{1 + SCR}

TF = \frac{1 - jω RC}{1 + jω RC}

∣ TF ∣ = \frac{1 + ω ^{2} R ^{2} C ^{2}}{1 + ω ^{2} R ^{2} C ^{2}} = 1

∠ TF = \frac{( tan ^{- 1} - \frac{ω RC}{1} )}{\frac{tan ^{- 1} ( ω RC )}{1}}

∠ TF = - 2 tan^{- 1} ω RC

solution:

F_{c} = \frac{1}{2 π RC}

100 = \frac{1}{2 π R ( 0.01 \times 1 0 ^{- 6} )}

R = 159.154 K Ω

1 + \frac{R _{2}}{R _{1}} = max Gain

assuming $R_{2}$ as 100 $K Ω$
assuming Gain as 2

1 + \frac{100 \times 1 0 ^{- 3}}{R _{1}} = 2

R_{1} = 100 K Ω

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