# Transistor types and polarities

Transistors are three-terminal devices capable of amplifying signals. They come in two broad classes, bipolar junction transistors (BJTs), and field-effect transistors (FETs). These notes are about BJTs.

BJTs have a control terminal called the base, and a pair of output terminals, called the collector and the emitter. A signal applied to the base controls the current flowing from collector to emitter. The collector current and the (much smaller) base current combine to form the emitter current. The base-emitter and base-collector junctions behave like diodes. Normally the base-emitter diode is conducting, whereas the base-collector diode is reverse-biased.

There are two BJT polarities available, NPN and PNP; for NPN devices the collector is more positive than the emitter, and the opposite is true for PNP.

NPN and PNP type transistors

These points are worth recalling:

VBE ≈ 0,6 V

IC ≈ IE

# Operating modes

One can think of a bipolar transistor as a current amplifier with roughly constant current gain β, or as a transconductance device for which the collector current is programmed by the base-emitter voltage.

Transistors can operate as switches, or they can be used as linear devices with an output current proportional to an input signal. Put another way, a transistor can be in one of three stages: cutoff (non-zero VCE but zero IC), saturated (non-zero IC but near-zero VCE), or in the linear region (non-zero IC and VCE).

## Current gain

In the simplest analysis, the transistor is simply a current amplifier, with a current gain called beta (β). For a typical BJT, β is supposed to be around 100, but it is only loosely specified, and a particular transistor type may have a large spread in specified beta at some collector current.

A current into the base causes a current β times larger to flow from collector to emitter, if the external circuit allows it:

$I_C = \beta \times I_B$

When currents are flowing through a NPN transistor, the base-emitter diode is conducting, so the base is approx. 0,65 V more positive than the emitter. The transistor does not create the collector current; it throttles current from an available supply voltage.

## Switch

When operated as a switch, a current must be injected into the base to keep the transistor “on”. This current must be substantially more than IB = IC / β. In practice a value of 1/10th of the maximum expected collector current is common. Under this condition the transistor is in saturation, with a VCE of 25-200 mV. At such low voltages the base-to-collector diode is conducting, and it robs some of the base-current drive. This creates an equilibrium at the saturation voltage.

# Ebers-Moll

The Ebers-Moll equation (and its simplified counterpart) shows the exponential relationship between VBE and IC (and thus an approximate VB). Collector current is determined by VBE and a parameter IS, the latter related to the transistor die size and its current density.

$I_C = I_S(T)(e^{\frac{V_{BE}}{V_T}} - 1)$

where

$V_T = kT / q = 25,3 mV$

at room temperature, q is the electron charge (1,6 x 10-19 coulombs), k is Boltzmann’s constant (1,38 x 10-23 joules/K), T is the absolute temperature in Kelvin, and IS(T) is the saturation current of the particular transistor.

## Transconductance

A BJT is a transconductance device. A transconductance device puts out a current that is proportional to an input voltage. In this sense, a BJT’s collector current IC is controlled by its base-to-emitter voltage VBE.

## re

A small-signal resistance re of about 25 Ω at a collector current of 1 mA is present at the emitter. It scales inversely with current.

## Rules of thumb

The following rules of thumb are handy :

• IC increases by a factor of 10 for a ± 60 mV increase in VBE.
• IC doubles for a ± 18 mV increase in VBE.
• IC increases 4% for a 1 mV VBE increase.

## Early effect

The Early effect describes the imperfection of a transistor current source. IC increases slightly with increasing VCE, this is called the Early effect. There are circuit configurations, such as degeneration, or the cascode, that alleviate the Early effect. The Early effect is often negligeable, but it can cause substantial errors in a current mirror that lacks RE‘s.

## Miller effect

The Miller effect can be a serious obstacle to design of high-frequency amplifiers. Miller effect results from capacitive feedback in any inverting amplifier, tending to oppose changes at the input.

# Important circuits

## Current source

A current source delivers a constant current regardless of the load’s voltage drop. VB determines VE which in turn fixes IE (VE/RE). Since IC ≈ IE the current source sinks a current IC from the load.

$I_C = (V_b - V_{BE}) / R_E$

Current source (sink)

A current source’s voltage compliance is the maximum voltage it will reach as it attempts to produce the desired current. It will fail when the transistor saturates, which happens a VCE of 25-200 mV.

## Emitter follower

The emitter follower is a linear amplifier with an ideal voltage gain of unity. The beta of the transistor increases the follower’s input impedance and reduces its output impedance. The dc output voltage is offset from the dc input by VBE, about 0,6 to 0,7 V. Cancellation circuits exist.

Split-supply emitter-follower, single-supply emitter-follower with biasing network, push-pull amplifier to cancel crossover distortion

Input and output impedances of an emitter follower:

$R_{IN} = (1 + \beta) \times R_E$

$R_{OUT} = (r_e + \frac{R_{SOURCE}}{\beta}) \parallel R_E$

## Common-emitter amplifier

The simplest common-emitter amplifier has a grounded emitter. The gain is then GV = – RC/re. This poses a problem: the gain is inverse in re, thus proportional to IC. But the latter changes with the load voltage, producing first-order changes in gain, leading to distortion. This can be alleviated by adding emitter degeneration in the form of an emitter resistor RE. The gain is then

$G_V = -\frac{R_C}{R_E+r_e}$

Adding an emitter resistor greatly reduces the effect of re.

Common-emitter amplifier, common-emitter amplifier with bypass capacitor for high gain at signal frequencies

Input impedance of the common-emitter amplifier:

$R_{IN} = R_{THEV_{BIAS}} \parallel (1 + \beta) \times (R_E + r_e)$

Input impedance for the common-emitter amplifier with bypassed emitter resistor:

$R_{IN} = R_{THEV_{BIAS}} \parallel (1 + \beta) \times r_e$

In both cases, the output impedance is:

$R_{OUT} = R_C$

## Differential amplifier

The differential amplifier is a symmetrical configuration of two matched transistors, used to amplify the difference of two input signals. It may include emitter degeneration, but need not. For best performance, the emitter pulldown resistor is replaced by a current source.

Differential amplifiers reject strongly any common-mode input signal, achieving good common-mode rejection ratio (CMRR).

Basic differential amplifier

The common-mode and differential gains of a differential amplifier are as follows:

$G_{CM} = - \frac{R_C}{2 \times R_{TAIL}+R_E+r_e}$

$G_{diff} = \frac{R_C}{2 \times (R_E + r_e)}$

CMRR equals to:

$CMRR = \frac{G_{diff}}{G_{CM}}= \frac{R_{TAIL}}{R_E+r_e}$

I hate loose sheets, and these pages are an attempt to bring order into my notes and thoughts. They are where I jot down circuit templates, formulas, and notes. Expect them to be full of errors, incomplete, and being updated frequently.