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Problem 2.13PP
A common connection for a motor power amplifier is shown in Fig. The idea is to have the motor 
current follow the input voltage, and the connection is calied a current amplifier. Assume that the 
sense resistor rs is very smail compared with the feedback resistor R. and find the transfer 
function from Vin to la. Also show the transfer function when Rf=
Figure Op-amp circuit for Problem
Step-by-step solution
step 1 of 3
A common connection for a motor power an^lifier is given. 
Sketch the given figure.
Step 2 of 3
At node A, write the voltage equation.
V L -0 ^
R
At node B, write the voltage equation, with R^-^ R 
, 0 - f% 0 - V . ,
R R,
^ r + r / ‘
step 3 of 3 ^
The d3mamics o f the motor is modeled with negligible inductance as J^9^ + 
We can rewrite as
4 , + * 4 = A'^.as +
At the ou^ut, &om the equation
, 0 - r . 0 - r . ,,
R 5 ,
j , e ,+ b e , = K,i^
And the motor equation 
Find To
V„ = l^R, + I^R^^■ K,
J^s -I- b
y — 0 V —0 V — 0
Substitute in the equation ------ 1- — = 0 and sinqjlify.
R^ Rj R
R^ 5 ,1 .* ■ • J , s ^ b ) R
This e^^ression shows that, in the steady state, when s —> 0 , the current is proportional to 
the ii^ut voltage.
We know that the current anq^lifier has no feedback from the output voltage, in which
And thus, we get
U _ R
y>.
Thus, the transfer fimction is obtained as ^ - - M l 
U R