# How can we find transfer function of this n/w

How can we find the transfer function $$\frac{E_0(s)}{E_1(s)}$$ of this RC network

simulate this circuit – Schematic created using CircuitLab

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Replace the capacitor C with an impedance of value $Z_c = 1/(Cs)$ and apply voltage division rule.

ie, $$E_0(s) = E_1(s) \times \frac{Z_c}{R+Z_c}$$

or, $$\frac{E_0(s)}{E_1(s)} = \frac{Z_c}{Z_c+R}$$

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$$\frac{E0(s)}{E1(s)}=\frac{\frac{1}{s \cdot C}}{R+\frac{1}{s \cdot C}} = \frac{1}{1+s \cdot C \cdot R}$$

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With resistor potential dividers like this: -

It's exactly the same for any impedance. On your circuit, the impedance at the bottom is $\dfrac{1}{s\cdot C}$ where s is $2\cdot\pi\cdot f$.

Therefore the transfer function is: -

$\dfrac{\dfrac{1}{s\cdot C}}{{\dfrac{1}{s\cdot C} + R}}$ and this reduces to: -

$\dfrac{1}{1+s\cdot C\cdot R}$

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