DP 3-5 The input to the circuit shown in Figure DP 3.5 is the voltage source voltage, v_s. The output is the voltage v_o. The output is related to the input by

The output of the voltage divider is proportional to the input. The constant of proportionality, g, is called the gain of the voltage divider and is given by

The power supplied by the voltage source is

Where

is called the input resistance of the voltage divider.

(a) Design a voltage divider to have a gain, g = 0.65.

(b) Design a voltage divider to have a gain, g = 0.65, and an input resistance, R_in = 2500 Ω.

Figure DP 3.5

If there are no other conditions then we have

So

Thus

or

So choose either resistor and you have the other from one of these equations.

(a) Design a voltage divider to have a gain, g = 0.65.

Pick an easy value for R₂ say 1000 Ω, then R₁ is

So solution is

(b) Design a voltage divider to have a gain, g = 0.65, and an input resistance, R_in = 2500 Ω.

So we have two conditions

and

using

Plugging this into the equation above we can solve for R₂

so

Then

There are many possible answers for Part (a)

One possible answer is

For Part (b)

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This page last updated on January 24, 2019