# How to calculate amplifier gain (in dB) using frequency?

I know how to calculate decibel gain using the ratio of power, or Vin/Vout.

However, is there a way to calculate the magnitude of the attenuation and phase angle when you’re given the cutoff frequency and another frequency?

• Calculate the transfer function with the amplifier configuration (ie inverting or noninverting) and the gain of your resistors (and filter caps). Apr 12 '18 at 16:57
• Did you mean "either ratio of power, or Vin/Vout", or "ratio of power, otherwise said Vin/Vout"? Apr 14 '18 at 7:58

No. Well, at least, not quite. The cutoff frequency only gives you pole behavior of your magnitude plot. I believe you're talking about the filter function where you basically perform a frequency sweep. However, depending on what the shape of the Bode plot, you can find a pattern from the magnitude plot. You haven't told us what filter this is nor its order so I am forced to give you an example.

If, for an example, you know that this amplifier circuit is a low pass filter, you can relate the frequency sweep and the cutoff frequency to the magnitude plot and phase plot.

Transfer function of the First Order Low Pass Filter:

$H(j\omega)=K\frac{1}{1+\frac{j\omega}{\omega_c}}$

Magnitude Plot (and skipping some algebra):

$M_{v-dB}=-10\log({1+\frac{\omega^2}{\omega_c^2}})$

Lastly, the phase plot of the of the magnitude plot is:

$\phi=-\tan^{-1}({\frac{\omega}{\omega_c}})$

The attenuation can be determined by your typical $V_{in}/V_{out}$ equation in dB.

Hence,

$K=(\frac{V_{in}}{V_{out}})_{dB}=10^{dB/20}$.

is there a way to calculate the magnitude of the attenuation and phase angle when you’re given the cutoff frequency and another frequency?

For any given filter topology yes there is. Consider a simple 1st order RC low pass filter. It has a transfer function (TF) like this: -

$$H(j\omega)=\dfrac{1}{1+j\omega RC}$$

From this simple formula you can find the cut-off frequency ($\dfrac{1}{2\pi RC}$).

And you can calculate phase angle at cut-off with a little more math

For any frequency you can calculate the magnitude of the TF and the phase angle too. Providing you have the TF you can do what you want.

If you don't know much about the filter (order, complexity etc..) then no, you can't.