High input impedance and low output impedance is an important terms of electronics circuits designs. In amplifier circuits it is often desirable. I am explaining this characteristic here taking an amplifier as an example.
You know that the gain of an amplifier is limited up to an extent. To have the highest amplified signal we desire the input signal to be appeared in the input of the amplifier without any attenuation (loss).
We will consider the circuit above to explain this phenomena. Let, V1 is the input signal or signal source to the amplifier; considered as 0.35 volt. As there is no source practically possible without any source resistance/impedance; let us consider resistor R1 (10 ohm) as source impedance whose value remains low /very low normally. The resistor R2 (10 ohm) is considered as the input impedance of the amplifier; this time it has a low input impedance (you see source & input impedance both are same). Tow voltmeter at two side shows the signal and input voltage. When I simulate this circuit, it draws 17.7 mA current (total resistance=20 ohm). It cause more drops across the source resistance R1 and nearly half of the signal (0.18×2=0.36) appears to the amplifier.
Now we consider for the above circuit where the input impedance R2 has a higher value (10 kilo ohm). In the simulation through ISIS (Proteus), It draws 0.03 mA current; 6 times less than before from the source as the total resistance is 10,010 ohm. In this case
10 ohm×0.00003 Ampere = 0.0003 Volt
drops across the source. So almost the full input voltage appears across the amplifier. So higher impedance ensures less drops of the input signal.
We know the amplifier amplifies the input voltage N times upon its ability. And we found that high input impedance ensures the full of the signal voltage to the input. That is why we desire high input impedance.
On the other hand, Output impedance is desired lower. Loads are connected at the output of an amplifier and we want maximum power at the load. That means we want maximum current to flow at the amplified voltage. By the above analogy, we easily understand that if output impedance is higher the more voltage will drop. When the load draw more current output voltage will vary more. This is not desirable. That’s why low output is desired.