Why is Z2 = Ra + (Rb || C) used instead of just Rb || C?

Because the HF gain 4 exceeds 1 and Ra sets it

To lower the DC gain below the HF gain

With pole 1/(RbC)=100, what gives the zero at 200 and hence Rb?

100(1 + Rb/(R1+Ra)) = 200, so Rb = 4R1

100(1 + Rb/R1) = 200, so Rb = R1

100(1 + Rb/(R1+Ra)) = 200, so Rb = 3R1

200(1 + Rb/R1) = 100, so Rb = 4R1

With C = 1 uF, what are R1, Ra, Rb?

R1 = 2.5 k, Ra = 7.5 k, Rb = 10 k

R1 = 10 k, Ra = 30 k, Rb = 40 k

R1 = 2.5 k, Ra = 10 k, Rb = 7.5 k

R1 = 7.5 k, Ra = 2.5 k, Rb = 10 k

Asked 4/26
2080 Bhadra · 4 marks

Non-inverting realization of 4(s+200)/(s+100)

Short answer

Using non-inverting topology with Ra, Rb||C: choose C=1 μF, then Rb=1/(100×1 μF)=10 kΩ, R1=2.5 kΩ, Ra=7.5 kΩ. Yields 4(s+200)/(s+100), HF gain4, DC gain8.

Design the following transfer function using non-inverting op-amp configuration T(s) = 4(s+200)/(s+100)

Given $T(s) = 4\dfrac{s+200}{s+100}$ : HF gain 4, DC gain $4\times2 = 8$ , zero at −200, pole at −100.

Non-inverting configuration: $Z_1$ from the inverting input to ground, $Z_2$ from output to inverting input:

T(s) = 1 + \frac{Z_2}{Z_1}

Because the HF gain is greater than 1, use $Z_1 = R_1$ and $Z_2 = R_a + (R_b \parallel C)$ :

T(s) = \frac{R_1 + R_a}{R_1}\cdot\frac{s + \frac{1}{R_bC}\left(1 + \frac{R_b}{R_1+R_a}\right)}{s + \frac{1}{R_bC}}

         +--Ra--+--Rb--+
         |      |      |
         |      +--||--+
         |         C   |
   +-----+-|-\         |
   |       |  >--------+--- Vo
  R1 Vin---|+/
   |
  GND

Matching:

\begin{aligned} 1 + \frac{R_a}{R_1} &= 4 \Rightarrow R_a = 3R_1 \\ \frac{1}{R_bC} &= 100 \\ 100\left(1 + \frac{R_b}{4R_1}\right) &= 200 \Rightarrow R_b = 4R_1 \end{aligned}

Choose $C = 1\ \mu$ F:

R_b = \frac{1}{100 \times 10^{-6}} = 10\ \text{k}\Omega,\quad R_1 = 2.5\ \text{k}\Omega,\quad R_a = 7.5\ \text{k}\Omega

Check: DC gain $= 1 + (7.5 + 10)/2.5 = 8$ . Correct.

Answer: $R_1 = 2.5\ \text{k}\Omega$ , $R_a = 7.5\ \text{k}\Omega$ , $R_b = 10\ \text{k}\Omega$ , $C = 1\ \mu$ F.

✓ Answer checked by Claude Sonnet 5.5

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