What are the voltage gain, input resistance, andoutput resistance of the amplifier as shownif R1 = 8.2 k ohm and R2 = 750 k ohm ? Express thevoltage gain in dB. i,R2R1

Given data, The value of resistance is R1 = 8.2 kΩ. The value of resistance is R2 = 750 kΩ By…

Answered: i, R2 R1

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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Question

What are the voltage gain, input resistance, and
output resistance of the amplifier as shown
if R₁ = 8.2 k ohm and R₂ = 750 k ohm ? Express the
voltage gain in dB.

Expert Solution

Step 1

Given data,

The value of resistance is R₁ = 8.2 k $Ω$ .
The value of resistance is R₂ = 750 k $Ω$

By virtual ground concept,

$V_{+} = V_{-} = V_{i}$

The expression for input resistance is,

$\begin{array}{rcl} R_{i} & = & \frac{V_{i} - V_{-}}{i_{1}} \\ = & \infty . . . . . . . . . . . . . . . . . . . . . . . . . . . since (current flowing through op amp that is i_{1} = 0) \end{array}$

Since $i_{1} = i_{0}$

The expression for output resistance is,

$R_{0} = \frac{V_{0}}{i_{0}}$

$\begin{array}{rcl} V_{0} & = & i_{0} (R_{1} + R_{2}) \\ = & i_{1} (R_{1} + R_{2}) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \sin c e (i_{1} = i_{0}) \\ = & 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \sin c e (i_{1} = 0) \end{array}$

Therefore,

$\begin{array}{rcl} R_{0} & = & \frac{V_{0}}{i_{0}} \\ = & \frac{0}{i_{0}} \\ = & 0 \end{array}$

By voltage divider formula,

$\begin{array}{rcl} V_{i} & = & V_{0} \times \frac{R_{1}}{R_{1} + R_{2}} \\ \frac{V_{0}}{V_{i}} & = & \frac{R_{1} + R_{2}}{R_{1}} \\ A_{V} & = & \frac{V_{0}}{V_{i}} = 1 + \frac{R_{2}}{R_{1}} \end{array}$

Where A_V is the voltage gain.

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