Announcements Assignment 2 due now Assignment 3 posted, due Thursday Oct 6 th First mid-term Thursday October 27 th

Lecture 9 Overview Transistors

Semiconductor device First Active circuit element - gain > 1 Discuss the Bipolar Junction Transistor only See Simpson Chapter 5 for more detail.

Bipolar Junction Transistors NPN Bipolar Junction transistor shown (PNP also possible) 3 terminals: Emitter, Base, Collector Contains 2 p-n junctions: emitter-base junction, collector-base junction Can be thought of as two back-to-back diodes, but operating characteristics are very different Base region (P-type here) must be thin for transistor action to work Base Emitter Collector

Modes of operation Use 2 voltage supplies to bias the two junctions (forward or reverse) 3 basic modes: cutoff, active and saturation, correspond to three different bias conditions. Base Emitter Collector “OFF” “ON”

Active Mode Collector-Base junction is reverse biased Emitter-Base junction is forward biased i C =βi B (β= ) Active circuit element - gain > 1 !! How does collector current flow when collector-base junction is reverse biased? Emitter CollectorBase + - iCiC iBiB iEiE V CE V BE

Active Mode What's happening? Emitter-base is forward biased; collector-base reverse biased. Forward bias of emitter injects electrons into thin base region Majority shoot through the base into the collector region where they encounter the voltage source on the collector and produce a current. Electrons combine with holes in the base region and form negative ions which impede the flow Drawing off negative charge via the base lead reduces this effect (“making the base smaller”) - so the base current controls the flow of electrons into the collector Nobel Prize 1956; Shockley, Bardeen & Brattain Direction of current flow + -

Bill Shockley Born 1910 London, England Died 1989 Stanford, California

Active Mode Can relate i B and i C β is defined mainly by the properties and geometry of the materials Ideally constant for any particular type of transistor Typically around 500 "Common-emitter current gain" Actually varies with temperature and emitter current Collector current is controlled by the base current

Emitter current Emitter current is the sum of i B and i C (KCL) where α is called the common-base current gain (~1.0)

Circuit Symbols and Conventions BJTs are not symmetric devices Doping and physical dimensions are different for collector and emitter Collector largest, connected to heat sink as most power dissipated there Emitter region smaller, and more heavily doped to provide an abundance of charge carriers Base region is very thin (~50nm) to enhance probability that electrons will cross it PNP devices also exist - diode senses are reversed, so bias voltage polarities must also be reversed

Emitter CollectorBase + - iCiC iBiB iEiE V CE V BE i-v Characteristics Simplest model for low frequencies (DC condition) "Ebers-Moll". Relates collector current I C to base-emitter voltage V BE : I S =Saturation Current Similar to Diode Law Recall I B =I C /β V BE ICIC Collector current is controlled by the base-emitter voltage V BE

BJT Amplifier To act as an amplifier, first bias the transistor to get it into active mode Then superimpose a small signal v be on the base Under DC conditions: Added resistor R C Note labelling scheme: i C =I C +i c "Common emitter" configuration

BJT Amplifier DC condition biases the BJT to the point Q on the plot Adding a small voltage signal v be translates into a current signal that we can write as: If v be /V T is small: So the small signal current is: g m is the "transconductance"; corresponds to the slope at point Q DC component I C Small signal component i c i.e. a voltage-to-current amplifier; small signal collector current determined by base-to emitter voltage

More on small-signals Base current also varies with v be So, having small signal voltage at the base, and small signal current at the base, consider the small signal equivalent resistance into the base, r π : Alternatively, rearrange to give small signal resistance between base and emitter, r e : I B =DC component of base current i B i b = small signal component of base current i B

Small signal models Use these relations to represent the small signal model for the transistor by an equivalent circuit. Hybrid-π model: e.g. as a voltage controlled current source: or as a current controlled current source

Small signal models Other small signal models may sometimes be more convenient. T model:

Using small signal models 1) Determine the DC operating conditions (in particular, the collector current, I C ) 2) Calculate small signal model parameters: g m, r π, r e 3) Eliminate DC sources: replace voltage sources with shorts and current sources with open circuits 4) Replace BJT with equivalent small-signal models. Choose most convenient depending on surrounding circuitry 5) Analyze

Voltage gain with small signal model To convert the voltage controlled current source into a circuit providing voltage gain, connect a resistor to the collector output and measure the voltage. Find the gain using a small signal model: v be icic rere RCRC icic vcvc eliminate DC sources and apply T- model

Voltage gain So, we have a voltage-to-current amplifier (a voltage controlled current source) To convert the voltage controlled current source into a circuit providing voltage gain, connect a resistor to the collector output and measure the voltage. So, small signal voltage gain:

Summary of useful equations Basic DC operating conditions: Add a small signal: