Plotting JFET source follower input capacitance in the function of frequency

Question

Hi, 
 I would like to plot the input capacitance (and the input resistance) of a jfet source follower circuit in the function of frequency . The input impedance is complex of course in the frequency range involved between 1 MHz and 10 MHz but I need help in doing this. 
 I used the 2N4416 jfet model and its input capacitance is known from data sheet (which is about 3-4 pF) but I wish to see it plotted on the vertical axis while the horizontal axis shows the frequency range. 
 Here is the schematic I use for simulation, together with the small signal AC simulation plot on the voltage output and I attached the asc circuit file too 
 
 JFET source follower tests 1.asc 
 
 Thanks for any help in advance. 
 Gyula

AndersIL · Accepted Answer

Made png files that are possible to insert in Word dokuments. Im sorry that the capacitance is so high as ca 16,2pF at 1MHz. 
 Do not know why, I removed the R8 resistor because the J1 IG can be read out in trace as Ig(J1). 
 The trace formula is Ig(J1)/(V(ugs)*2*3.1454*frequency) 
 BR 
 Anders I L)

mtwieghr · Answer

The circuit input impedance at the jfet gate is Zin = Vg/Ig. This gives a value of -j230kohm at 1MHz, equivalent to 0.69pF of input capacitance . 
 If you instead measure Zgs = Vgs/Ig, then this gives a value of 840 - j9740 ohms, roughly 16.3pF. But this is not a meaningful measure of an actual capacitance. It's not the input capacitance of the circuit and it's not a capacitance of the JFET itself. 
 With the 1uF capacitor added from source to gnd, both Zin and Zgs become -j70.3kohm, equivalent to 2.3pF. This 1uF capacitor effectively makes the JFET common source (and common drain). This circuit isn't useful though, it's just meant to show that you can measure the Ciss spec in the datasheet. 
 As for the units in the y axis label, there is a way to change that. You can actually put units in the waveform equation. Adding *1V/1A*1Hz cancels out the weird units, leaving a unit-less result. I don't think it's possible to get the units in farads though. 
 See attached. 
 6180.JFET source follower tests 1alsoluton2.asc 
 JFET source follower tests 1alsoluton2.plt

mtwieghr · Answer

So the JFET's Ciss is composed of Cgs + Cgd. I don't know exactly what these values are for the 2 N4416. In a common drain circuit like your, when you put an AC voltage Vg on the gate, the gate-drain voltage is also Vg (because the drain voltage is fixed). But the source voltage follows the gate voltage closely (that's what a common drain amp is supposed to do). That means Vgs is actually much smaller than Vg. Therefore Cgs draws almost no current, and does not contribute to the capacitance seen looking into the gain. 
 In your simulation, the voltage gain of the common drain stage V(s)/V(g) is 0.958 at 1MHz. That means for every 1V of AC voltage of Vg, Vgs only experiences (1-0.958)=0.042V of AC swing. That means the effect of Cgs on Cin is reduced by a factor of 0.042, which means it's pretty much insignificant. Go ahead and try adding 100pF between g and s, you'll probably see Cin rise by roughly 4.2pF. The 0.69pF left over is almost entirely from Cgd. 
 edit: oh, actually another reason you might not be seeing Cin increase. If your equation is still using Ig(J1), then that's not going to be affected by the external capacitance. Instead use the current through R8, that will see both the JFET's own capacitance and the external capacitance. 
 See attached. Shows that with 100pF of Cgs added, overall Cin becomes 4.82pF at 1MHz, just as expected. 
 JFET source follower tests 3.asc 
 JFET source follower tests 3.plt

AndersIL · Answer

The formula is right but it gives the Rin of the jfet not the Rin of the circuit

AndersIL · Answer

Hi 
 I suggest that you add 2 e voltage/voltage elements UC1 accross the C1 capacitor and UGE accross the JFET both with gains 1 
 And then you do add trace with the formula V(uc1)/V(uge)*10 (it gives 15,8pF at 1MHz)Then you get the capacitance in dB nF 
 Im not sure if this is the correct formula but it is a try this is the capacitance including the miller capacitance The capacitance XC is about 1/1000 the 10Meg Resistance at 1MHz at 10 Meg it is 1/100 
 Anders I L

AndersIL · Answer

I shall not be UGE it should be UGS for the JFET 
 Anders I L

AndersIL · Answer

JFET source follower tests 1alsolutontran.pdf 
 JFET source follower tests 1alsoluton.asc

AndersIL · Answer

JFET source follower tests 1alsoluton2.asc JFET source follower tests 1alsolutontran2.pdf 
 Hi 
 This is the right formula based on the Ugs/Ig=XC=1/(2*pi*f*C) 
 Cgs=16.2pF 
 Anders I L

AndersIL · Answer

Hi 
 The 10 Meg resistor is 1/1000 at 1MHz and 1/10000 at 10Meg not 1/100 of the XC of the CGS

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Plotting JFET source follower input capacitance in the function of frequency

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