# Voltage Divider

What is the most used tool by the Electrical Engineers? Of course memorization (Talking in case of Nepal. I do not know about other places.). Memorization is good until you have to memorize fewer things. However, after reading a few pages, the number of stuff you have to memorize becomes enormous. If you think, there are very little things you have to memorize. There is some stuff like Ohm’s law, Kirchhoff’s current and voltage law which you should commit to memory. Other stuff can be deduced from these principles during necessity.

Today I am talking about the simple circuit “Voltage Divider”. Although it is a simple circuit it is a very important one. Here important does not mean its frequency of appearance in the final exams is high. What I mean by important here is if you understand its basic and use it as a tool you can solve a very complicated circuit without increasing the pressure in your cranium.

This is the most common voltage divider you see in most textbooks. The gain of this circuit is H.

H= \dfrac{R_{2}}{R_{1}+R_{2}}

(You can not ignore this, once you study control system.)

The transfer function of this circuit is given by the relation (Apply KVL you will arrive at this.)

\dfrac{V_{out}}{V_{1}}= \dfrac{R_{2}}{R_{1}+R_{2}}

This is the circuit that passes the percentage of input to the output. This percentage is depended on the gain of the circuit. By adjusting the value of the resistors, the gain can be changed.

You will see the interesting things after you start to play with this circuit. For example, think about what will happen if we replace the resistor R_{2} with the capacitor or with the inductor (I will think about replacing with the capacitor). What do you think? Is this circuit still a voltage divider or something else? Yes, it is called the RC circuit but if you think capacitor as a resistor whose value depends on the frequency it is indeed a voltage divider circuit whose gain depends on the frequency.

Feed the step input to this circuit. Step input is the rapid change in the input voltage. What will the responses of these elements? The resistor is emotionless about the change in the supply voltage but the capacitor is little touchy with the rapidly changing voltage. There was a smart guy named Joseph Fourier who found that fast change in voltage is composed of high-frequency signals. The impedance of the capacitor is given by the relation \dfrac{1}{2\pi f C}. This means the capacitor has low impedance for the high-frequency signals. If you think carefully now you know the reason why your circuit analysis teacher has told you to short circuit the capacitor initially.

If you supply AC as input now this circuit acts differently. This circuit is now called Low Pass Filter. When the frequency goes up from low to the high, the capacitor behaves openly and gradually moves to short. If you know the voltage divider and the frequency response of the capacitor you will notice this circuit passes low frequencies and block high frequency. That is why this circuit is called a low pass filter. The drawback of this circuit is that it is subjected to a phenomenon called loading. The loading can become a great topic to post for the future. Similarly, a low pass filter can be constructed using the inductor but I will save it for future posts.