Another Way to Measure Transistor Gain

We've talked about hfe, which represents current gain, but there is another way to measure gain in a transistor. Some devices, like vacuum tubes or FETS, don't draw any input current, so the concept of current gain makes no sense. For those devices, engineers use the term "tranconductance," which is a fancy way of saying how much the output current changes when you change the input voltage. BJTs also exhibit transconductance, which gives us another way to evaluate gain. Remember we talked about how hfe has pretty large manufacturing tolerances and varies from device to device? Transconductance is just the opposite. It's extremely predictable and is the same for every part number, silicon and germanium! That's because transconductance in BJTs is a fundamental property of solid-state physics. Transconductance is represented by the symbol gm. gm is easily calculated; it is collector current divided by the Thermal Voltage (vt), which is about 26mV at room temp: gm = ic / vt. For example, a transistor with a collector current of 520uA would have the transconductance 520uA / 26mV = 20mS (milliSiemens). Conductance is measured in units called Siemens (go ahead, get your snickering out of the way). Siemens is the reciprocal of Ohms. A 1K resistor has a conductance of 1/ 1K = 1mS. To calculate the voltage gain of a transistor stage, we multiply the transconductance by the load resistance. Suppose the transistor in the previous example has a 15K load resistor. Its voltage gain would be 20mS * 15K = 300. Ok, so it's not quite that simple because BJTs have output impedance which is effectively in parallel with the load resistance. We can get a pretty good estimate of a transistor's output impedance by dividing 50V by the collector current. It's just a rule of thumb, but it's plenty accurate for what we're doing. The transistor in the previous example has a collector current = 520uA, so the output impedance is approx. 50V / 520uA = 96K. We put that in parallel with the 15K load resistor and get 13K, so the voltage gain is actually 260. Notice that hfe plays no part in calculating transconductance or voltage gain. A germanium transistor with hfe = 50 has the same transconductance as a silicon transistor with hfe = 800, as long as their collector currents are the same.

Two more quick thoughts related to transconductance and we'll call it a day.

If we know hfe & gm, we can calculated the input impedance (Zin) of a transistor. Zin = hfe / gm. Let's say the transistor in the previous examples has hfe = 200. Then Zin = 200 / 20mS = 10KΩ.

The output impedance of an emitter follower is low, but how low? That's easy to calculate. The output impedance (Zout) of an emitter follower is Zout = 1 / gm. Using that same transistor as an emitter follower: Zout = 1 / 20mS = 50Ω.

Next time: What's All This Impedance Stuff About?
 

fig

Village Idiot
Help me out here man...

Is hfe (the references in the article) AC voltage gain?

..and..

"voltage gain would be 20mS * 15K = 300"

Again, is this AC voltage?

Thanks for all the contributions. They are appreciated.
 

Barry

Well-known member
Man I'm going to need to read over that a dozen or so times, my head is spinning
 

Chuck D. Bones

Circuit Wizard
Help me out here man...

Is hfe (the references in the article) AC voltage gain?
No. The hfe is AC current gain. In other words, it's how much the collector current changes for small change in base current. Not the same as voltage gain. Voltage gain and current gain in a transistor are basically independent quantities. You might want to check out my article on hfe.


"voltage gain would be 20mS * 15K = 300"

Again, is this AC voltage?

Yes.
 
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fig

Village Idiot
No. The hfe is AC current gain.
Doh...my ignorance is obvious, but is unmatched by my curiosity. I'll re-read the hFE/hfe articles as well as some further reading. I don't want to abuse this resource with nonsensical questions.
 

Chuck D. Bones

Circuit Wizard
No problem, it's a lot of info to digest.

Think of it this way: Electronic circuits have two intertwined variables: voltage and current. Once we've built the circuit and taken our fingers off of the switches and pots, those are the only two variables. The circuits we build are all about controlling the relationship between voltage, current and time.
 

BurntFingers

Well-known member
No problem, it's a lot of info to digest.

Think of it this way: Electronic circuits have two intertwined variables: voltage and current. Once we've built the circuit and taken our fingers off of the switches and pots, those are the only two variables. The circuits we build are all about controlling the relationship between voltage, current and time.

Can I interest you in some of this?

 

HamishR

Well-known member
I get stuck on the expression "in and of itself" - what does that actually mean?? So if I get stuck on that, what hope do I have understanding anything else they say? Another one is when people say "if you will" - if I will what?

There is no hope for me. Just tell me what to build and I'll do it.
 
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fig

Village Idiot
I get stuck on the expression "in and of itself" - what does that actually mean?? So if I get stuck on that, what hope do I have understanding anything else they say? Another one is when people say "if you will" - if I will what?

There is no hope for me. Just tell me what to build and I'll do it.
Consider if you will, that in and of itself the phrase bears no context
 

fig

Village Idiot
I don't know what you're asking.
...maybe this way..

Do the Zin and/or Zout values have any influence on the design of a transistor stage?

Your explanation of those calculated values made me wonder if they (the impedances) were anticipated in the design, and if so are nominal values substituted (such as a median tolerance)?
 
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