# Diodes, their use in mixers and taylor approximation

In https://en.wikipedia.org/wiki/Frequency_mixer#Diode, it talks about diode's current-input voltage relationship, and using Taylor approximation of e^x demonstrates frequency mixer abilities.

But this works only if input voltage is small. But I also heard that frequency mixers can operate for large-voltage signals. How is math being done there?

1. Add another term to the Taylor series and evaluate it in either a computer algebra system (Mathematica or Maple or Maxima) to find when the higher-order terms become significant.

2. Simulate your circuit under transient analysis in a SPICE-like simulator, and look for higher-order terms.

Keep in mind that when "unwanted" terms fall well outside the desired output band (for example, $3\omega_1$, $2\omega_1+\omega_2$), they'll be relatively easy to filter out. The terms that cause practical problems are the ones that fall near the desired output band (for example $3\omega_1-\omega_2$, assuming the input frequencies aren't widely separated)