**CALCULATING CATHODE FOLLOWER INPUT RESISTANCE
Richard Matthews
Leeds Radio**

Brooklyn NY

718 963-1764

The treatment given assumes the following:

a) the input signal does not drive the grid too close to 0 volts (ie no
grid current)

b) the circuit is operating below, say 40 khz.

Input and output signals in cathode follower are in phase. To see this,
imagine what would happen if you were to apply a positive going pulse between
grid and ground; the plate current would increase. When the plate current
increases, the voltage across Rk also increases (with the side of Rk connected
to the cathode becoming more positive with respect to ground). Think of
the voltage between the grid and cathode terminals as v_{in'}. It
is clear that v_{in'} + v_{rk1} +v_{rk2}
= v_{in} (by kirchoffs voltage law) You may now think of a cathode
follower as a amplifier that uses 100 percent of its output voltage as series-negative
feedback.

**(1)** Cathode Follower Gain = µ(R_{k})/(R_{p}+(µ)(R_{k}))

The above equation is true when circuit is not externally loaded. For
gain with external load substitute R_{k}| |R_{L} (Where
R_{L} is the external load.)

It can be seen that

**(2)** lim_{Rk->inf }µ(Rk)/(Rp+(µ)(Rk))
= 1

and so an assumption that we will use later is sound, and not a "rule of thumb".

For component identification, please refer to diagram at the bottom of page.

**We will define:**

v_{in} = the amplifier input voltage

Av = voltage gain

Rin = small signal input resistance

i_{in}= input current

**(3)** i_{in} = (v_{in} - v_{x})/R_{g}

**(4)** Rin = v_{in}/i_{in} = v_{in}/(v_{in}-v_{x})/R_{g}
= v_{in}R_{g}/(v_{in}-v_{x})

**(5)** v_{x} = v_{in}*Av*(R_{k2}/(R_{k1}+R_{k2}))

From **(2) **we know that Av is approximetely equal to 1.

So:

**(6)** Rin = v_{in}R_{g}/ (v_{in}-v_{in}(R_{k2}/
(R_{k1}+R_{k2}))

factoring out v_{in}

**(7) **R_{in}= R_{g}/(1-R_{k2}/(R_{k1}+R_{k2}))

Note how when R_{k2}= 0, that Rin = R_{g}