I'm studying this app. note on frequency discrimination method to measure phase noise.
In page 35, appendix A, there are these equations:
The input to the transfer function is \$\Delta f\$ and output is \$\Delta V\$. What happened to the
\[
\sin\left[2 \pi\; f_m \left(t – \frac{\tau_d}{2} \right) \right]
\]
term when writing the equation for delta V?
Sorry if it is too obvious. I just could not see why.
Best Answer
The whole point of the frequency discriminator is to have some output voltage which depends on the frequency shift \$\Delta f\$. In time domain you have this signal at the output of the discriminator:
\[ V(t) = \Delta V(\Delta f) \cdot \sin\left[2 \pi\; f_m \left(t - \frac{\tau_d}{2} \right) \right] \]
I.e. you have a sinusoidal signal whose amplitude holds the information about the frequency variations of the input. Therefore, in a system perspective, the relationship between your "input" \$\Delta f\$ and the desired output \$\Delta V\$ is independent of the sinusoidal signal time variations.
In other words, by "transfer response" it is meant the relationship between the amplitude of \$V(t)\$ versus \$\Delta f\$.