Answer to Question #152329 in Electric Circuits for Lawrence

Question

Standard Resistors (kΩ)
1.1 1.2 1.5 1.8 2.2
2.7 3.3 2.9 4.7 5.6
6.8 8.2

You are to design a non-inverting amplifier circuit. One of the external resistors (R1) has value of 100Ω. Determine the resistance of the 2nd external resistor (R2), which would produce a gain of 44. Then draw the resistor circuit using the standard resistors to get as close as you can to the desired value.

Answer 1

Explanations & Calculations

• The functioning equation for a non-inverting amplifier is given as

$\qquad\qquad \begin{aligned} \small V_{out}&= \small \bigg(1+\frac{R_{feedback}}{R_{input}}\bigg)V_{in} \end{aligned}$

• When the gain to be 44,

$\qquad\qquad \begin{aligned} \small 1+\frac{R_f}{R_i}&= \small 44\\ \small \frac{R_f}{R_i}&= \small 43\\ \small R_f &= \small 43R_i \end{aligned}$

• Even the sum of all the given resistors cannot fit in the given equation along with the $\small 100\Omega$ resistor, it is easy to figure out that $\small R_f=100\Omega$ & other resistors should compensate the value of $\small R_i=\large \frac{100}{43}=\small 2.32558\Omega$

• During the selection, it is to be known that the series connection of resistors gives an equivalent value greater than the value of the largest resistor whereas a parallel connection produces an equivalent even less than the value of the smallest resistor.

• Value of R_i is given as follows

$\qquad\qquad \begin{aligned} \small \frac{1}{R_i}&= \small \frac{1}{8.2\Omega}+\frac{1}{6.8\Omega +\frac{(2.2\Omega\times3.3\Omega )}{(2.2\omega+3.3\Omega)}}+\frac{1}{2\times 2.7\Omega}\\ \small R_i&= \small \bold{2.3240 \Omega} \end{aligned}$

• Then the gain is

$\qquad\qquad \begin{aligned} \small &=\small 1+\frac{100\Omega}{2.3240\Omega}\\ &= \small 44.029 \end{aligned}$