The Junction Field Effect Transistor was invented in 1923 by Julius Lilienfeld and patented in 1926, but was not practically implemented until many years later because the techniques of purifying and doping semiconductor materials were not perfected then in order to make a working device.
The Transistor and Field Effect Transistor were reinvented and perfected in Bell Labs much later.
The above diagram (Fig. 1) explains in a simplistic pictorial way how a junction F.E.T. works. The electric field produced by the gate controls the amount of current flowing through the drain to the source of the F.E.T.
There is no current flowing in the gate at any time, the n type semiconducting material of the gate and the p type material of the drain and source create a reverse biased junction that has a depletion layer very much like a reverse biased semiconductor diode.
The consequence of this is the F.E.T. has very high input impedance indeed. A property very much desired when designing an audio amplifier or any circuit where you don’t want to load the input signal.
A very good article written and available on the net by Mike Martell explains in some detail how to design a two stage junction F.E.T. amplifier. Well worth reading as it is not too mathematical and it works very well in practice.
The above circuit diagram (Fig. 2) can be designed if you follow his article.
Input impedance of the amplifier is determined by the value given to R3 it has negligible effect on the operating conditions of the F.E.T.
When the biasing conditions are correct then the voltage gain becomes R1/R2.
Placing a bypass capacitor across R2 will increase the gain substantially at the expense of increased noise and distortion.
The output impedance is effectively equal to R1 in parallel with the load it is driving.
Because of the high input impedance of the circuit the capacitor value of C1 should be a comparatively small value.
The capacitive reactance of C1 should be about 1/10th the value of R3 at the lowest frequency desired to be amplified.