Hello again,
One way to do this is to look up the curve for the transistor in the data sheet. We can then solve for the diode parameters N and Iss in:
Ib=Iss*e^(Vbe/(N*VT))
The collector current is then:
Ic=Ib*Beta
and with a base resistor Rb from Vin to base, collector resistor Rc from collector to Vs, and feedback resistor Rf from collector to base the circuit equation for the base current is:
Ib=(Vin-Vb)/Rb+(Vc-Vb)/Rf
and the collector voltage is:
Vc=Vs-Ic*Rc
Combining those equations we come out with a single equation:
-Vs-(Rf*Vin)/Rb+(Rf*Vbe)/Rb+Vbe+e^(Vbe/(N*VT))*Iss*Rf+Beta*e^(Vbe/(N*VT))*Iss*Rc=0
We then perturb this by changing Vin to two different levels that are not too different, and calculate Vbe for each level. We get two solutions we'll call simply Vbe1 and Vbe2. Inserting those solutions into the exponential equation for the base current, we get two base currents we'll call simply Ib1 and Ib2, respective to each Vbe. We can then calculate the input resistance as:
Rin=(Vbe2-Vbe1)/(Ib2-Ib1)
This is still an estimate and of course it may change a little depending on what the value of Rb is as that is the resistance we might see in the output of the previous stage. It will also change depending on the other resistors of course, and even the level of the power supply voltage Vs. So it is just an estimate and subject to change depending on the other changes in circuit components and power supply.
A typical value found with N=1.37 and Iss=1e-12 and VT=0.026 and Rb=10k and Rc=1k and Rf=100k was Rin=around 400 Ohms. This will vary with the type of transistor too as N and Iss will change, and so will the ambient temperature.