For the system shown in below figure- what is the transfer function VosVis-Given R1-R2-C1-C2-1 unit

After taking Laplace transform, the series combination of R_1 and nbsp;C_1 gives: R_1+1sC_1 Similarly, the parallel combination of nbsp;R_2 and nbsp;C_2 ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Control Systems

Definition of Transfer Function

For the syste...

Question

For the system shown in below figure, what is the transfer function $\frac{V_{o} (s)}{V_{i} (s)}$ ?

(Given $R_{1} = R_{2} = C_{1} = C_{2} = 1 u n i t$ )

\frac{V_{o} (s)}{V_{i} (s)} = \frac{s}{s^{2} + 3 s + 1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{V_{o} (s)}{V_{i} (s)} = \frac{1}{s^{2} + 3 s + 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{V_{o} (s)}{V_{i} (s)} = \frac{s^{2}}{s^{2} + 2 s + 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{V_{o} (s)}{V_{i} (s)} = \frac{s + 1}{s^{2} + 2 s + 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{V_{o} (s)}{V_{i} (s)} = \frac{s}{s^{2} + 3 s + 1}$
After taking Laplace transform, the series combination of $R_{1}$ and $C_{1}$ gives:
$R_{1} + \frac{1}{s C_{1}}$

Similarly, the parallel combination of $R_{2}$ and $C_{2}$ gives:
$\frac{\frac{R_{2}}{s C_{2}}}{R_{2} + \frac{1}{s C_{2}}}$

Substituting, $R_{1} = R_{2} = C_{1} = C_{2} = 1$ makes the above combinations $1 + 1 / s and \frac{1 / s}{1 + 1 / s}$

On applying the voltage divider rule, we get

$V_{o} (s) = \frac{\frac{1 / s}{1 + 1 / s}}{1 + \frac{1}{s} + \frac{1 / s}{1 + 1 / s}} V_{i} (s)$

$\frac{V_{o} (s)}{V_{i} (s)} = \frac{\frac{1}{s + 1}}{\frac{s (s + 1) + (s + 1) + s}{s (s + 1)}}$

$\frac{V_{o} (s)}{V_{i} (s)} = \frac{s}{s^{2} + 3 s + 1}$

Suggest Corrections

Similar questions

Q. For the system shown in figure below, what is the transfer function

\frac{V_{o} (s)}{V_{i} (s)}

Q. In the figure shown below,

R_{1} = 1 Ω, R_{2} = 2 Ω, C_{1} = 4 μ F, C_{2} = 2 μ F

, the time constants (in

μ s

) for the circuits

I, I I

and

I I I

respectively are

Q. For the compensated attenuator of figure, the impulse response under the condition

R_{1} C_{1} = R_{2} C_{2}

Q. Three Circles with centres

C_{1}, C_{2}, C_{3}

and radii

r_{1}, r_{2}, r_{3}

where

r_{1} < r_{2} < r_{3}

are placed as shown in the figure.
Then,

r_{2} =

_________.

Q. In the circuit shown in figure,

R_{1} = 1 Ω, R_{2} = 2 Ω,, C_{1} = 1 μ F, C_{2} = 2 μ F

and

E = 6 V

. Calculate charge on each capacitor in steady state.

Join BYJU'S Learning Program

For the system shown in below figure, what is the transfer function Vo(s)Vi(s)? (Given R1=R2=C1=C2=1 unit)

For the system shown in below figure, what is the transfer function $\frac{V_{o} (s)}{V_{i} (s)}$ ?

(Given $R_{1} = R_{2} = C_{1} = C_{2} = 1 u n i t$ )