# Would leakage through a JFET create thermal noise

The impedance through the gate of a JFET is very high and leakage current very small. Would this impedance act like a large resistor creating thermal noise?

Would this be a low noise way of implementing a large impedance?

• As a rule in the world us mortals experience (as opposed to laboratory experiments by physicists testing reality), Johnson noise exists for any Ohmic resistance. This follows directly from statistical thermodynamics. So it's not easily escaped when dealing with large populations of atoms and molecules. The leakage current at the JFET gate (usually operated reverse-biased) will also have shot noise. Shot noise is a current noise. Johnson noise is a voltage noise. But both of these can be "referred" to a common basis of either voltage or current to get a total. But nature doesn't allow cheating. – jonk Jul 18 at 22:06
• There are differences at different frequencies of operation and for different ways of matching up with sensor physics. In some cases, it would be better to use a JFET for specific sensors than using a BJT. But no bright line tells you that the JFET is always lower noise than a BJT for the first stage that couples with a transducer's physical behavior. If all you are looking for is a large impedance you are almost certainly better off just getting a really good resistor with noise dominated by Johnson noise and not others related to its materials and manufacturing. – jonk Jul 18 at 22:13
• people developing low-noise JFET phono-cartridge interface circuit (RIAA) also found JFET gates would have "tunneling" noise between drain and gate thru the reverse-biased gate-diode. Instead of operating at 35 volts, they used a bipolar cascade atop the JFET, with the bipolar base at about 10 voltes. As an additional benefit, the Cmiller dropped from 300pF to 20pF, and the high-frequency cartridge response became more ideal. This was on diyAudio.com. – analogsystemsrf Jul 19 at 6:54

Jonk's comments are right on the money, so for the most part I'm restating, but also adding a few minor bits.

Would this be a low noise way of implementing a large impedance?

Nope, in fact it would be modestly worse:

• Thermal noise is $$\4kTR\Delta f\$$, i.e. thermal noise is directly proportional to the resistance. If you have a large resistance, you have a lot of noise.
• ...plus a JFET will also give you shot noise as well.
• ...and last (and perhaps least) a JFET will give you flicker noise (1/f noise) too. At high frequencies you probably won't notice the effect of flicker noise but at lower frequencies it could matter.

A nice overview of these various types of noise in JFETs can be found in this application note (from 1976!).

Bottom line, if your goal is "high impedance with low noise" then you're best off with a plain old resistor, where your only noise is thermal, versus a semiconductor which will introduce these other peculiar types of noise in addition.