 # How to calculate the Gain and bandwidth of a common emitter amplifier using LTspice

### Calculation of gain in linear scale

Voltage Gain of  an amplifier is the ratio of output voltage to the input voltage .i.e Vout / Vin.

This post is a continuation of the previous post which explains the frequency response of a common emitter amplifier. You can refer the details like circuit diagram, input and output voltage waveform and frequency response in the previous post.

Here, Vin =40mv. Vo is the out put voltage which is obtained from the frequency response plot. Frequency response is plotted in semi-log. i.e log f (frequency) in x axis and gain( in db) in y axis.For calculating gain in linear scale, first you need to convert the plot in linear scale. To achieve this, right click on the y axis and you will see a pop up screen. Select “Linear” from the three options shown. Then we will get the plot in linear scale which is shown in below.

First, we need to calculate the maximum output voltage Vout and the maximum frequency Fm. To find this first left click on the Vout label in the plot (on top of the screen) and a pop up form will appear. In this window you can see the frequency , magnitude and phase values. You will also see a dotted line corresponding to x and y axis. In order to find the maximum voltage, just drag the dotted line using the mouse. Then check the values in boxes as it will change as you move your mouse across the screen. Adjust your mouse pointer so that you get maximum values for magnitude(voltage).

We can display the value of voltage and frequency on the plotting plane itself. You need to select “Plot Settings” from the menu bar and then select “Notes & Annotation”. Then select the first option “Label Cur Pos” from the sub-menu. It will write the values on the plot as shown in the below figure.

In the above example, we got fm = 128.6144 khz, and Vout = 3.270875.

Gain = Vout/Vin.= 3.270875/40mv

Gain is 81.77.

### Calculation Of Gain in db

The equation for calculating Gain in db= 20 log Vout/Vin.

The procedure for calculating gain in db is similar to the calculation of gain in linear scale. Follow the same steps explained in the above section. The only difference here you need to select the decibel scale in Y axis.

Output voltage in db= 10.29328. so the gain= 20 log 10.29328/40mv =48.

### Calculation of Bandwidth

The equation to calculate the Bandwidth is B.w= Fh-Fl.

Fh is the upper cut off frequency.

Fl is the lower cut off frequency.

To find the cut off frequency first find the 3 db points.i.e =maximum output  voltage -3 db, Here maximum output =10.29328. So Vout-3db =7.29328. Mark the values in plot using your cursor. Refer the below screenshot.

From the figure Fl= 272.39081 khz

Fh= 47.377214 Mhz

Bw= Fh- Fl =47.104 Mhz.

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