# What is meant by “input/output impedence” of a transistor stage in amplifiers?

I am studying BJTs (bipolar junction transistors)(npn), different types of amplifiers built with these transistors and their small signal equivalents (hybrid $\pi$ - model without capacitances) but I don't understand some of the phrases I encounter.

Example: I am studying ASCE-stage (anti-series common emitter configuration) (also known as differential stage) at this moment and its small signal equivalent.

I have not mastered the biasing of transistors yet, hence minimalistic amplifier stage:

ASCE-stage:

Small signal equvalent:

According to the book, ASCE-stage has "high input impedance". Like, I don't understand where that impedance is being "measured". Do you just "measure" it across the input terminal of the small signal equivalent? What is its impedance then?

I have been trying to understand that for a while now and I would appreciate any advice I receive.

• Usually you apply, in the linearized circuit, a small input test voltage and measure (compute) the input current. The math is your friend. For common_emitter, Rin is beta*1/gm. – analogsystemsrf May 25 '17 at 17:32
• @analogsystemsrf .Thank you for your imput. What is "beta" in your expression above? – Clone May 25 '17 at 18:07
• It comes from the linearized (there is a non-linear large-signal version, from which the linearized small-signal version derives) hybrid-pi model. It is better explained here: en.wikipedia.org/wiki/Hybrid-pi_model . Just look for the symbol, $r_\pi$, on that page. – jonk May 25 '17 at 20:53
• "beta" in bipolar devices is the ratio of collector_current/base_current, when transistor is not in saturated nor in avalanche regions. That is, the Vce is > 0.5 volt and < Vcbo. Learning to compute amplifier behavior, using the linearized small-signal bipolar params, is enormously empowering. Go for it. Ask questions. – analogsystemsrf May 26 '17 at 2:28
• @analogsystemsrf Is the input impedance $=r_{pi}$ and the output impedance $=r_{0}$ then? – Clone May 26 '17 at 7:29

Input impedance in this context refers to "small-signal input impedance". Before I offer an intuitive explanation of what that is I will explain what it is NOT:

It is NOT: 1. Put a battery across it. 2. Look how much current flows. 3. Call the ratio of the voltage to the current the impedance.

Again it is NOT this. To see why, consider a simple example. What is the input impedance of a capacitor? If you put a battery across it and tried to measure the current, you'd measure infinity. But of course we know that we characterize a capacitor as having an input impedance of 1/(jwC). If you don't understand this last bit, don't worry.

Small-signal input impedance is this.

You WIGGLE a node voltage up, and you watch how large the corresponding WIGGLE in the current that rushes away you is.

I like water analogies and despite the fact that they seem silly I think they're a very useful first step in developing intuition for electronics.

Consider a long hose with a water balloon at either end. A red balloon on one end and a blue balloon on the other. Suppose that this system is filled with water.

Imagine you give the red balloon a light squeeze, the blue balloon will get bigger as water is displaced from the red balloon, through the hose, into the blue balloon.

The ratio of how hard you squeezed to the amount of water wooshing the hose as you squeeze is the impedance! Notice that, like a capacitor, an impedance is defined even though no "DC" water flows.

Now make the hose thinner and apply the same pressure as before. What happens? You squeeze but less water rushes away because the hose resists.

When I look at circuits I imagine myself standing on the node, bending down, yanking it up, and watching how much current "rushes away" from me. If it's a lot of current, I know that node has a low impedance. If it's a little bit of current, that node has a high impedance.

Combine this intuitive explanation with the commonly available definitions given in textbooks which are more mathematical in nature and you'll be on your way.