Plate Resistance & Amplification Factor for JFETS & D-MOSFETs

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Don't FETs Have Plate Resistance (RP)? What About Amplification Factor (Mu, µ)? • NOTICE. On this page, we're talking about JFETs and depletion MOSFETs. Not enhancement MOSFETs. Not any other variety of FET. (FETs are a large family, and not all “cousins” behave the same way.)

Are FETs really like tubes? The short answer is YES! As preamplifiers, JFETs and depletion MOSFETs behave a lot like pentodes. There are depletion power FETs that act the like tubes, too. For example, the DN2540 by Microchip.

How do triodes compare? For those who love triode tubes because of their lovely, even harmonics: Every JFET comes with a built-in Triode Mode. So does every depletion MOSFET. We'll go into these ideas later on this page. For now though, the bottom line is this: Nothing is exactly like a tube, except another tube. But JFETs and depletion MOSFETs are as close as semiconductors come. And that truth makes them attractive. Plus, they have their own advantages...

Further questions. Still, if you're technical, you have further questions. That's why we're here. Please read on...

Why don't FETs have an R_P or a Mu (µ) rating? Datasheets often do offer some of this data. But unfortunately, manufacturers bury the data. Here, we reveal how to recover this obscure information. You can then apply Hendrik van der Bijl's famous tube formula to FETs. (1.) This is the formula...

µ= (GM x RP)

Where µ= Amplification factor or Mu GM= Transconductance RP= Plate Resistance

When we apply the formula to FETs, it becomes...

µ= (GM x RD)

Where RD= Drain Resistance

Of course, FET datasheets don't include R_D. Yet Malvino points out that drain resistance R_D is the reciprocal of output transconductance, the variable G_OS. And variable G_OS does appear on many datasheets. (2.) (Note that some datasheets name this same variable Y_OS. Nothing like standardization!)

Amplification factor, µ doesn't appear. But now, we can calculate it!

First, we adapt the formula to what we find on datasheets...

µ= [GM x (1 / GOS)]= (GM x RD)

Where GOS= Output Transconductance Transconductance (GM)= Inverse Resistance

Example...

Compare that example to a vacuum tube...

Fair play. Actually, the “JFET-tube comparison” above isn't exactly fair. Sure, a JFET has three electrodes, just like a triode does. But the JFET normally behaves like a pentode. That statement assumes that the drain potential is above the pinch-off voltage. Then the device is a voltage-controlled current source, a “pentode.” (With the drain below the pinch-off voltage, the device is a voltage-controlled resistor, a “triode.” The same rules apply to depletion MOSFETs.)

Beyond pinch-off, the JFET drain (plate) voltage ceases to affect drain current. Instead, the drain current remains constant. This behavior is the way a pentode acts, but unlike triode behavior. And the 12AX7 that we used in our example is a triode. So let's rethink the 12AX7 comparison, and check out the performance of a pentode, the 6J7...

Maybe a bit more like our JFET. The 6J7 has a high plate resistance and high transconductance, just as our JFET has. Possible conclusion: The JFET is “just like” a pentode. But not so fast! Unlike a pentode, our JFET has two modes of operation. So far, we've only looked at one of these. Here are the two...

1. Pentode, or Constant-Current Mode, the usual state.

2. Triode, Ohmic, or Linear Mode, where the device behaves like a triode.

Coping with incomplete data. In a minute, we'll have more about Triode Mode. But first, we need to solve another problem that might have occurred to you: What if your datasheet doesn't include a G_OS rating? How can you obtain the drain resistance value? Answer: There's a simple trick with Ohm's Law.

Using Ohm's Law If your datasheet doesn't provide the GOS value, you can still find the drain resistance. Use Ohm's Law this way (3.)... Refer to the drain curves graph, right. Pick a drain curve. (In our example, the -0.4V curve.) Pick two drain voltage values on the desired curve.

Fig. 1. Pick ID & VD values on the drain curve graph. (Here, using Triode Mode curves.) (4.)

4. Drop down to the X-axis, and check that the drain voltages are what you wanted. (In our example, 1V and 2V.)

5. Compute the difference between the two voltage values.

6. Pick two drain current values on the desired curve.

7. Move left to the Y-axis, and check that the drain currents are what you wanted. (In our example, 3.0 mA and 3.8 mA.)

8. Compute the difference between the two current values.

9. Convert the difference mA to A (Divide by 1,000).

10. Divide the voltage difference value by the current difference value (in amps). The result is your AC plate resistance at the selected points. (Below is the formula.)

Use Ohm's Law

RD= (ΔVD / ΔID) Example (with values from Fig. 1) High Low Dif Rd 2V 1V 1V 1,250 3.8mA 3.0mA 0.8mA Calculations (0.8mA / 1,000)= 0.0008A RD= (1V / 0.0008A) RD= 1,250Ω

• NOTICE The symbol Δ stands for “a change in.” We also know this symbol as “delta.”

Pentode Mode Example Finding RD inside Pentode Mode may be more difficult than in Triode Mode. The reason for the difficulty is the flatness of the curves in Pentode Mode. Yet there is some slight curvature. To achieve a meaningful RD value, choose widely separated voltage and current points. See the red lines in the example, right. (5.)

Fig. 2. Pick ID & VD values on the drain curve graph. (Here, using Pentode Mode curves.) (6.)

How do engineers harness the Triode Mode? How can I build a Triode-Mode preamp? Visit our next page!

1. Alfred A. Ghirardi, Radio Physics Course, 2nd ed. New York: Technical Division, Murray Hill Books Inc.: 1932, 419. ▶Re: Vacuum tube formula relates transconductance, amplification factor, and plate resistance.

2. Albert Paul Malvino, PhD, Electronic Principles, Second Edition. (New York: McGraw-Hill Book Company, 1979), 330. ▶Re: Parameter G_OS is the reciprocal of drain resistance.

3. George J. Christ, Radio Tube Fundamentals, Bradley, IL: Lindsay Publications, 2008, 24-27.
(Original Publisher: NY: Gernsback Publications, Inc., 1951.)
Short URL: shorturl.at/imrS4 (Reprint edition)
Short URL: https://is.gd/Oeln3Z (Original edition)
Order One: tinyurl.com/mr37t8d4 (Amazon.com listing)
▶Re: How to derive AC plate (drain) resistance from characteristic (drain) curves for the JFET. Example uses Triode Mode area of curves.

4. Vishay Siliconix, 2N3819, document 70238, S-04028, Rev. D (Sunnyvale, CA: Vishay Siliconix LLC, 2001).
▶Re: My datasheet overlay demonstrates how to find variable values for the Ohm's Law calculation of R_D. The Datasheet is for a type 2N3819, N-channel JFET. The original manufacturer was Siliconix. Siliconix obsoleted the part, but other semiconductor foundries still manufacture the 2N3819. Examples: Central Semiconductor, InterFET, and On Semiconductor.

5. Christ, Radio Tube Fundamentals, 24-27.
Short URL: shorturl.at/imrS4 (Reprint edition)
Short URL: https://is.gd/Oeln3Z (Original edition)
Order One: tinyurl.com/mr37t8d4 (Amazon.com listing)
▶Re: Deriving AC value of R_D in Pentode Mode area of curves.

6. Vishay Siliconix, 2N3819, document 70238, S-04028, Rev. D.
▶Re: My datasheet overlay demonstrates how to find R_D in Pentode Mode.

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I_DSS FINDER

I_DSS TESTER

D-FET CURVE DESIGN-1

D-FET CURVE DESIGN-2

TUBE SOUND WITH DEPLETION FETS

DIY TRIODE-MODE PREAMP WITH FET

Contents

• Are FETs Really Like Tubes?

• Pentode Mode vs. Triode Mode

• Find the AC Value of R_D

• Footnotes

Figures

• Fig. 1. Graph: Pick I_D & V_D

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