# Explain small signal model of transistor to a beginner [closed]

I am a little weak in analog circuits even though electronics is my subject (Engineering course). Transistor is like a Pandora box to me. Last day I read a question about how to use transistor as switch in this site. It made complete sense to me. That gave me confidence to learn more about transistors. I want learn deep about that now. Deep enough so that I can even do analysis myself without referring any textbooks. So please explain me about transistor models in plain English.

I know what transistor is. What I dont know is about its models for circuit design like hybrid model, small signal model etc. I dont what equations (I got books for that). Tell something in plain language.

EDIT: Explain about Small signal model.

• What transistor are you interested in? MOSFET, BJT, JFET, IGBT? Are you looking for a signal level analysis or a fundamental model focusing on how the carriers inside the device behave? – SimonBarker May 22 '11 at 10:10
• @Simon- about simple BJT. I have seen portions like h-parameters, small signal models etc in my syllabus and have used them extensively in the last 2 semesters for analysis. But still I dont have an idea about them. Textbook are not making any sense to me. They all start with those complicated math stuff. So please give me good start so that later on I can refer those book again. – 0xakhil May 22 '11 at 10:27
• You should ask specific questions. This one should be closed. – Leon Heller May 22 '11 at 12:28
• okey I will edit it. – 0xakhil May 22 '11 at 12:34
• The Hybrid-Pi model? This is like pulling teeth! – Leon Heller May 22 '11 at 12:44

These small signal models are important if you want to characterize the frequency response of whatever amplifier you end up building with these transistors. In a lot of applications, it is not enough to just know the gain for a given DC input.

Suppose I have built myself a common-emitter amplifier out of a BJT for the purpose of amplifying an audio signal. Let's say I've added my decoupling and bypass capacitors and biasing circuit as well. How would I go about determining whether or not my amplifier ends up attenuating 15 KHz signals? How would I determine if my signal output at 40 Hz is strong enough? For the purpose of amplifying audio, these frequencies are important to consider.

The gain is not uniform across all frequencies and this is due to the inherent capacitance and resistances inside the BJT itself. Thus we need to construct these models that closely resembles the transistor's internals for the purpose of performing circuit analysis on paper (or in CAD, if your tools allow) that will tell us if our amplifier design is suitable for our application or not. The parameters you speak of are usually given in the transistor's datasheet such that you can plug them in to one of the commonly accepted small signal models and perform your calculations.

A BJT(bipolar junction transistor) is a device that can amplify current. They have a gain($h_{fe}$ when referring to BJTs) which is what the current on the base is times by to get the current through the collector. They have 3 legs:
- Base
- Emitter
- Collector

There are 2 types of BJTs:

• NPN - current goes in to the base allowing current to from from the collector to the emitter.
• PNP - current comes out of the base allowing current to flow from the emitter to the collector.

For a NPN Transistor with gain of 400 and Current on the base is 0.05mA. The current then going through the collector is:

$I_{c} = h_{fe} * I_{b}$
$I_{c} = 400 * 0.05$
$I_{c} = 20mA$

The emitter current can be calculated by adding the collector current and the base current:
$I_{e} = I_{c} + I_{b}$

When using a BJT it is important to have a resistor in series with the base between 1k and 2k2 as too much current can cause damage to the BJT.

To turn the transistor on a voltage of around 0.6V to 0.8V needs to be applied to the base($V_{be}$), this is so that current can flow.

• I got about 1/4 of the way typing up what Dean just posted. So I'll pull that out and just respond with this. One of the best things you can do for your understanding is to pick up a copy of The Art of Electronics 2nd Edition. It is a pricey book, but has a great chapter walking through transistors that would be of great help to you. – Joe May 22 '11 at 12:02
• Okey, maybe I should edit my question. I know these things. Tell me what is h-parameters? What is its significance? – 0xakhil May 22 '11 at 12:03
• As I said previously, ask your teachers. Why don't you do that? – Leon Heller May 22 '11 at 12:12
• Ahh ok yes reword the question to get an answer to suit the question you want as I understood it to be what is a transistor - the basics. – Dean May 22 '11 at 12:14
• @Leon I don't mind writing that as thats my revision for BJTs for my exam next month :D. – Dean May 22 '11 at 12:15

Here is a good description of the small-signal BJT model. Some maths is inevitable in electronics, if modeling is involved. If you don't understand something in the presentation, ask about it, and an answer might be forthcoming.

Small signal refers to signals with small amplitutudes from the signal source (and we consider low frequencies for our model here)

When our signal is big, we can use linear algebra to analyse signals behavious around our Q point. We can use line functions and draw graphs (and usually consider the middle point on the Q line for maximum swing of the input signal)

But when dealing with signals of small amplitutde those models wont work. That is when we come to think of a transistor as a bipolar circuit with four heads.

There are many ways to refer input i and v of a bipolar to its output i and v. For transistors we use v1=f(i1,v2) and i2=g(i1,v2). Now the variables in both functions are the same.

Since current and voltage have v=ri relationship, we can consider the following :

V1= h11*i1 + h12*v2

I2= h21*i1 + h22*v2

Now think about the above equations, the first one is addition of two voltages and the second one is addition of two currents. Two voltages are added in a circuit when connected in series and two current are added together when connected in parrallel.

That is how you draw a circuit using the above equations, replaing the internals of a transistor in a circuit for small signal input.

Each h type is either a coeffient, impedance or admitance based on the show relationship.