If I put my notes here, I might be able to find them again later!
Supermatched JFETs
Truth be told, for a self-biased jfet audio circuit like the CrystalFET the main reason we need to used matched jfets is to ensure that the signal gain is the same in both channels. The operating point of the amplifier stage (the voltages and currents) can be allowed to vary a little so long as the transconductance, g_m is the same, as this is directly proportional to the open loop voltage gain, A, as
A = g_m R_l (transconductance x load resistance)
Now, yes, ideally you would find two jfets with identical saturation current and pinch off voltages, ensuring not just the same gain but also the same operating point. In practice though you are usually binning parts that are close to each other based on some reference parameter like the pinch off voltage (V_gs0) that you hope closely correlates with the signal gain. This is not quite as good though as the calculating the actual transconductance of the particular device in the circuit it is to be used in. And since I can do this**, I figured: why not?
It allows for devices with slightly different transfer curves but the same circuit gain to be paired together. It is an efficient and accurate way of obtaining close gain match between channels.
The DC operating point should be pre-screened (bin to V_gs0, for example) so that the circuit voltages and currents are not wildly different.
The table below shows some J113 which have been pre-screened for V_gs0 around 1.5-1.6 V. Most pairs match to within 1% transconductance.
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** transconductance, g_m = 2 sqrt(I_dss x I_ds) / V_gs0
[the derivative of the transfer function at I_ds]
If the saturation current is a little larger and the source drain current is a little smaller, the transconductance can balance out to the same value.
The only "trick" in the process is calculating I_ds from V_gs0, I_dss, and R_source.
I_ds = I_dss (1 - V_gs/V_gs0)^2 [jfet transfer function]
V_gs = I_ds x R_source [ohms law]
so
V_gs / R_source = I_dss (1 - V_gs/V_gs0)^2
rearrange to the form ax^2 + bx + c = 0 with x=V_gs and solve the quadratic expression using x = (-b +\- sqrt(b^2 - 4ac)/2a.
A = g_m R_l (transconductance x load resistance)
Now, yes, ideally you would find two jfets with identical saturation current and pinch off voltages, ensuring not just the same gain but also the same operating point. In practice though you are usually binning parts that are close to each other based on some reference parameter like the pinch off voltage (V_gs0) that you hope closely correlates with the signal gain. This is not quite as good though as the calculating the actual transconductance of the particular device in the circuit it is to be used in. And since I can do this**, I figured: why not?
It allows for devices with slightly different transfer curves but the same circuit gain to be paired together. It is an efficient and accurate way of obtaining close gain match between channels.
The DC operating point should be pre-screened (bin to V_gs0, for example) so that the circuit voltages and currents are not wildly different.
The table below shows some J113 which have been pre-screened for V_gs0 around 1.5-1.6 V. Most pairs match to within 1% transconductance.
_____
** transconductance, g_m = 2 sqrt(I_dss x I_ds) / V_gs0
[the derivative of the transfer function at I_ds]
If the saturation current is a little larger and the source drain current is a little smaller, the transconductance can balance out to the same value.
The only "trick" in the process is calculating I_ds from V_gs0, I_dss, and R_source.
I_ds = I_dss (1 - V_gs/V_gs0)^2 [jfet transfer function]
V_gs = I_ds x R_source [ohms law]
so
V_gs / R_source = I_dss (1 - V_gs/V_gs0)^2
rearrange to the form ax^2 + bx + c = 0 with x=V_gs and solve the quadratic expression using x = (-b +\- sqrt(b^2 - 4ac)/2a.
Total Comments 5
Comments
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Hi rjm,
at the moment I'm trying to curve-trace my 6 Semisouth SICs, so I had to read alot to fill my gap of knowledge and also to not set them on fire.
I learned that there are some ways to find out a JFet's Transconductance, and that for me it would be best and easiest to just variate the GS Voltage and to log the ID and VGS.
So, your table looks for me interesting, like another gap of knowledge to fill.
What exactly do you measure and how do you calculate the rest? I found the many times referred to papers here at diyaudio, but there are variations in how to calculate some parameters. For me this seems to be some sort of practical/theoretical gap.
I would be really happy if you could show me how your are doing this, and if you are so kind, please say something about the limitations, if there are any.
Regards,
MatthiasPosted 29th March 2016 at 01:28 PM by Murdoc
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Hi Mattias,
I'm calculating I_dss and V_gs0 using a two-point measurement technique explained in my previous post.
Using I_dss, V_gs0, and the source resistance R_s, I calculate the source drain current, I_ds.
The transconductance g_m is calculated from I_dss, V_gs0, and I_ds.
All this work is based on the ideal jFET transfer function of I_ds = I_dss (1 + V_gs/V_gs0)^2.
While your approach of plotting I_ds vs. V_gs is the most rigorous and accurate, if the transfer function above holds true then you don't need to such lengths. You can just measure two points on the curve to get the I_dss and V_gs0 parameters.Posted 29th March 2016 at 11:09 PM by rjm
Updated 29th March 2016 at 11:15 PM by rjm -
Hi,
I don't like people who don't read the whole stuff -- and now this also "happens" to me, sorry for that!
Thank you very much for your explaination!
Do you have ever compared your approach, which seems to be used from a lot of persons (in slighly other variations), and the curve tracing method?
Otherwise, you have chosen the method you described here very nicely, so there are good reasons to use it, despite it saves a lot of time.
Is there a big variation in praxis from the JFets mathematical formula/curve? And if so, is it relevant?
Thank you so much for your patience!
I just curve traved power JFets, and after checking my measurements twice, I saw that I had a too big variation. It wasn't the room temperature, but I learned that if the pressure with which the JFet is screwed to the heat sink varies, for a given V_GS the I_D also varies. So I have to choose of finding a way to fix them at a constant pressure, or, to maximize it's I_D while I vary the screw's torque. The last idea seems to be more practical, because I don't want to just measure the JFets, they should be mounted one day in a working amplifier!
This is my motivation on diggig deeper in measuring JFets.Posted 31st March 2016 at 04:13 PM by Murdoc
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I did make some edits in the main text in response to your earlier comment. Sorry if that caused confusion.
As long as the two measurement points are close to (bracket) the circuit operating point it doesn't matter if the actual transfer curve deviates from the simulated one at other places on the curve. The estimated I_dss and V_gs0 might be slightly off, but the transconductance and DC voltages will be correctly estimated for the circuit operating point.
iirc real transfer curves do vary slightly from the simple quadratic formula close to pinch off.
The real issue is that JFETs parameters change so much with temperature. There is little point making a super-accurate measurement if 2 C change in temperature will make it all for nothing. I think the best attitude is "go in, make a quick estimate, get out" and not to dwell on accuracy overmuch.Posted 31st March 2016 at 11:13 PM by rjm
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Hi!
I re-checked my measuring setup once again, even if it is really simple. Just because the pressure, with which the JFets are pressend on the heatsink, changed I_D.
I found out that my cables for measuring, even if they are quality Hirschmann cables, had a slightly corrosion on the connectors. I cleaned them, and got reliable measurements. One mystery solved.
Edit:
I'll do also the math with your procedere, and see how it varies. I hope that the difference will be just of academic nature, so I'll safe lot's of time in the future!Posted 4th April 2016 at 12:58 PM by Murdoc
