Diodes are electronic devices made from semiconductor materials such as silicon. In their pure form, these materials do not conduct electricity and are electrical insulators. But by adding a small amount of either p or n-type impurity, excess positive or negative charges are introduced into the bulk semiconductor. This charge is free to travel as electrical current, leaving behind fixed ions of the opposite charge bound in the crystalline lattice of the semiconductor material.
By placing n and p-type material together, a p-n junction is formed, as shown below.
This is a diode. Upon joining p and n materials, positive charge (called "holes") and negative charge (electrons) diffuse into the opposing material where they encounter opposite charges and recombine; their charges cancel. As charges diffuse, they leave behind fixed charges which tend to impede further diffusion. As holes diffuse into the n side of the junction, they leave fixed negative ions which tend to counter the diffusion of electrons moving into the p material. Like charges repel. The fixed charges produce an electric field which opposes diffusion and results in a region in which few mobile charges exist. This is the space-charge layer or p-n junction.
The symbol and electrical behavior of diodes is shown below:
The arrow part of the symbol is the p side and the vertical bar is the n side. When a dc voltage of about 0.7 V or more is applied in the forward direction (with the arrow of the diode symbol), current flows. When the voltage is less than 0.7 V (including reverse or negative voltage), no current flows. The positive applied field repels mobile holes, driving them toward (and across) the junction, overcoming its opposing electric field barrier. Electrons are similarly repelled toward the junction and cross it, recombining with holes. More charge flows into the diode to replenish recombined holes and electrons and external current flows. If the externally applied voltage polarity is reversed, mobile charges are attracted to the + and - applied voltages and away from the junction. This further depletes the regions around the junction of charge. Where there is no charge, bulk silicon is an insulator and does not conduct. No holes and electrons cross the junction to recombine and no external current flows.
The diode voltage-current (or v-i) relation is shown in the plot below: Above about 0.7 V of forward voltage, the current increases quickly and is very sensitive to diode voltage. It is difficult to control diode current by attempting to carefully adjust the forward voltage. Instead, a resistor is usually placed in series with the diode to a voltage source, as shown below:
Because the supply voltage (12 V) is so much larger than the diode voltage (0.7 V), most of its voltage is dropped across the resistor, which dominates in setting the current. The dc operating-point of 0.7 V and 11.3 mA are the bias voltage and current of the diode.
Bipolar Junction Transistors
Transistors are two diodes joined with a very thin common region, the base. When the base-emitter (b-e) junction is forward biased, mobile charges from the emitter cross the b-e junction. Some recombine, resulting in base current. But because the base is so thin, most cross the base-collector (b-c) junction, which is reversed-biased. The charges from the emitter are minority carriers in the base and are attracted across the b-c junction to become collector current.
What makes transistors so useful as circuit elements is that a small amount of base-emitter current controls a larger amount of collector-emitter current. A small electrical input can be amplified by a transistor.
This kind of transistor is the bipolar junction transistor (BJT). The two polarities of BJTs are npn and pnp. Their symbols are shown below:
Each has three terminals: base, emitter, collector. A small amount of current flowing into (out of) the base of an npn (pnp) causes a flow of currentb times larger from collector to emitter (emitter to collector), in the direction of the arrow. That is,
ic =b× ib
Beta (b) is typically about 100 in small-signal transistors and 20 in power BJTs. The base and collector currents join in the emitter so that
ie = ib + ic = (b + 1)ib
A small amount of base current thereby controls a larger amount of emitter and collector current. The base current results from a forward-biasing base-emitter voltage, vBE.
By Ohm’s Law, v/i is a resistance. What is the resistance of a diode? From the above v-i curve,
Rd = 0.7 V/1 mA = 700W
This resistance is the inverse-slope (1/slope) of a line from the origin to the point (0.7 V, 1 mA) on the diode curve. This is the static (or dc) resistance. For a small variation of voltage around 0.7 V, the change in current is much larger (lower resistance). This dynamic (or ac) resistance is the inverse-slope of a line tangent to the curve at the operating point, which is (0.7 V, 1 mA). Dynamic resistance is calculated from the solid-state equation for p-n junctions as:
where i is the diode current. For the given operating point (i = 1 mA), rd is 26W for small changes around the operating point. This diode dynamic resistance is much smaller than the static resistance.
BJTs have two diodes (or p-n junctions): base to emitter and base to collector. In an npn BJT, the b-c junction is normally reverse-biased. When it is forward-biased, the base is 0.7 V greater (more positive) than the collector. This state is called saturation. When BJTs are used as switches (as in digital or computer circuits) they are either off (no b-e or b-c forward bias) or else "full on" (saturated: b-e and b-c forward biased). For linear amplification, the b-c junction is reverse-biased (off) and the b-e junction is forward-biased (on). Both input and output waveforms have a range they must stay within.
A simple one-transistor amplifier can be built as shown below, using both positive and negative supplies:
This circuit has two loops: input and output. For the input loop, a change in the input voltage vin causes a change in voltage across RE and the transistor b-e junction dynamic resistance, re. To find re the static emitter current must first be found before the dynamic resistance can be calculated. (See the equation for rd above.) Therefore, solving transistor or diode circuits (those with nonlinear elements) has two steps:
To solve for the static currents and voltages, we observe first that if Vbe of the transistor is about 0.7 V and vin has no static voltage component (VBE = 0 V), then the - 5V supply is applied across 0.7 V in series with RE. This circuit is similar to the previous diode circuit, where RE largely determines emitter current. In this case, it is about (5 V - 0.7 V)/1.0 kW or 4.3 mA. The base current is IE/(b + 1) or (for b = 99) 43 mA. The collector current is the emitter current less the base current. The ratio of collector to emitter current is called alpha (a), defined as
Forb = 99, a = 0.99. Then IC is (0.99)× (4.3 mA) = 4.26 mA. This current drops (4.26 mA)× (2.2 kW) or 9.37 V across RL so that the collector voltage (to ground) is:
VC = 12 V - 9.37 V = 2.63 V
This is greater than the base voltage (0 V) and the b-c junction is reversed biased as required for linear operation. The static voltages and currents have now been determined and dynamic analysis can proceed.
The dynamic emitter resistance is 26 mV/IE or about 6W. The total resistance across which vin is applied is the transresistance rM:
rM = re + RE = 6W + 1.0 kW » 1.0 kW
Because re varies with temperature and static emitter current, in good design it is dominated by RE, a stable resistor, so that rM is stable; it affects the amplification or voltage gain (Av) which is:
Av = vout/vin
where vout and vin are dynamic voltages.
The significance of rM is that it determines the emitter current:
rM = vin/iE
The emitter current does not flow in the base circuit, where the input voltage is applied. The current goes somewhere other than through the input voltage source, vin. Consequently, rM is a "transfer resistance" or transresistance. And transistor is short for "transfer resistor."
Now that iE is calculated from vin and circuit elements of the input loop, iC is justa× iE and the change in voltage it causes across RL is
vout = - RL×a× iE
The minus sign is the polarity of the voltage change at the collector (to ground). An increase in collector current causes an increase in voltage drop across RL which subtracts from the collector supply (12 V), causing a decrease in collector voltage. We have worked our way from input to output. Putting the above equations together, the gain is:
Besidesa, the gain is a ratio of two resistances, the collector (or "load") resistance and the transresistance.
This is the general form of amplifier gain expressions. For our example, Av » - 2.2. The output voltage range is about ± 3 V and is limited by saturation at its minimum and cutoff (zero collector current) at its maximum. This design is saturation limited. For maximum linear dynamic range (largest undistorted output waveform), the collector voltage operating point would be about 6 V, halfway between saturation and cutoff. Calculation of saturation must also take into account base voltage, which is maximum (positive, not zero) when collector voltage is minimum. It is found from the gain expression.
A BJT circuit model for a transistor biased in the linear region of operation (a dynamic model for small variations around the operating-point values) is shown below:
The collector is connected to a current source controlled by the base current. Collector voltage variations across the current source (which has infinite resistance) do not affect the collector current. The collector is thereby isolated from the base-emitter input circuit. The key model element is the dependent current source, which provides amplification.
The dynamic base resistance is not re, though it is across the base-emitter terminals. Base resistance is greater because the collector current also flows through re in response to base current. The resulting base-emitter dynamic resistance can be derived as the "b transform" formula:
This equation says that resistance from the base will beb + 1 times larger than that in the emitter. This applies to all resistance through which the emitter current flows. In the amplifier circuit of last section,
or (100)×(1006W), somewhat more than 100 kW.
The output resistance of the above amplifier (from collector to ground) is that of a current source in parallel with the load resistor, RL. Current sources have infinite resistance (appear as open circuits), leaving the load resistance as the output resistance. The significance of input and output resistances is discussed in "Basic Amplifier Circuits."
The collector characteristic curves for an npn BJT are shown below. The collector current is plotted as a function of collector-to-emitter voltage, with base current as a parameter, stepped byDIB for each new curve. These curves are plotted by an instrument called a transistor curve tracer. Note that for these curves, the 50 mA base current curve is at about the 5 mA collector-current level. The b is therefore about 5 mA/50 mA, or 100.
The collector curves are not flat but increase slightly with collector voltage. For the given transistor model, the curves would be flat because the collector current-source’s current output is not affected by the voltage across it. But actual transistors are better modeled by including a resistance (ro) from collector to emitter. It typically has a large value and can usually be disregarded. The collector curves slope downward toward the left and intersect the vCE axis at - VA, the "Early voltage":
VA is typically 50 V. Then for IC = 1 mA, ro = 50 kW.
A second feature of the collector curves is that they voltage "saturate" below (in this case) 0.1 V. This suggests that the base-collector diode becomes forward biased at a vCE of 0.1 V, or VCB = 0.5 V.
For pnp BJTs, the curves are similar but currents and voltages are of opposite polarity. Such curves are found in the third quadrant (negative vCE, negative iC) with negative iB. Having both polarities of transistors leads to greater flexibility in circuit design.
Field-effect transistors (FETs) operate differently than BJTs. Instead of a base, there is a gate to which a voltage is applied. This voltage creates an electric field across a channel between drain and source. As the gate-to-source voltage varies, the resistance of the channel varies. Unlike BJTs, no gate current flows and the input resistance is infinite. Junction FETs (or JFETs) have a diode between gate and source which must be kept reverse-biased for linear operation. Instead of a reverse-biased diode gate, metal-oxide semiconductor FETs (or MOSFETs) have a metal gate separated by a thin glass (silicon-dioxide) layer of insulation over the channel. Both JFETs and MOSFETs have the same dynamic model, shown below with their symbols.
The FET model is simpler than that of the BJT. It is a voltage-controlled current source in its linear region of operation. Compared to a BJT,a = 1 and rs is analogous to re but typically has a larger value, around 100 W. A FET can be substituted for a BJT in the above amplifier circuit and, using these correspondences, dynamic analysis is similar. P-channel devices have the same polarity of gate (base), source (emitter) and drain (collector) as pnp BJTs.
JFETs are depletion-mode devices because they conduct (iDS ¹ 0 mA) with zero gate-source voltage. But almost all available MOSFETs are enhancement-mode devices; they are off with zero gate-source voltage. When vGS is around 5 V for MOSFETs (or > 12 V for power MOSFETs), they are "full on" and operate in the resistance region. This corresponds to the voltage saturation region of a BJT. The difference is that the channel (drain-to-source) resistance varies somewhat linearly with vGS.
FETs are characterized by a threshold voltage (pinch-off voltage for JFETs), VT, of usually about 2 V. For n-channel FETs, if the drain voltage remains greater than the gate voltage by VT, the transistor will operate in the linear region, where the above model applies. To bias FETs, a dominating source resistor (RE >> rs) returned to a supply much larger than the threshold voltage will determine source current and the gate-source voltage will be whatever corresponds to that current. This approach is essentially the same as that for BJTs except that base-emitter voltages (around 0.7 V) are smaller than the gate-source bias voltages of FETs, which can be over a volt. For linear operation, the drain (on n-channel devices) must be kept sufficiently above the gate voltage. The dynamic source resistance rs can be found in the device specifications (data book) as 1/gm.
Power transistors have large emitter/collector areas to handle large currents and/or voltages. Their packages are made to mount on heat sinks, to conduct away heat generated by power dissipation in the transistor. Linear amplifiers operate transistors in the linear region (and not as switches) with relatively high power loss. These inefficiencies are minimized by switching transistors between voltage saturation (low voltage, high current) and cutoff (high voltage, no current). For both on and off states, either transistor (collector/drain) voltage or current is near zero. By Watt’s Law for power, with units of watts (W),
P = v× i
and P » 0 W. Switching reduces power loss because P is zero (or nearly so) in both states. During the on state, transistor c-e or d-s voltages are not zero and conduction loss occurs. Also during switching, neither voltage nor current are near zero and for the brief time it takes to switch between states, switching loss occurs. It increases proportionally with both switching frequency and the switching time.
For high-power applications, control of power is achieved by switching transistors on for a fraction of the switching period, D, called the duty ratio:
As D is varied, the average output voltage and current is D× V and D× I, where V and I are the off-voltage and on-current. Linear control of the average values is thus obtained by this scheme for switching transistors, and is called pulse-width modulation (PWM). It is commonly found in motor and other actuator controllers and in power converters such as switching power supplies.
A newer power device, the insulated gate bipolar transistor (IGBT) has MOSFET input and BJT output characteristics. It has gate, emitter and collector. BJTs are capable of higher current densities than FETs while MOSFETs have no dc gate current. The disadvantage of IGBTs is that they have an additional output series p-n junction, with its additional voltage drop. Therefore, IGBTs are superior for c-e voltages exceeding 200 V. MOSFETs switch fastest, then IGBTs, and BJTs are slowest.
Low-power or small-signal transistors usually come as discrete components in TO-92A packages. Power transistors come in TO-220, TO-247 or TO-204 packages, shown below, with terminals identified:
Not all BJTs in TO-220 packages have the above pin-outs of their terminals (though most do). TO-247 cases are larger than TO-220, but with roughly the same shape. TO-204 packages mount on a flat metal plate with holes for base/gate and emitter/source terminals, and two holes for bolts that hold transistor, socket and heat sink (which could be the plate) onto the mounting plate. Insulators are often required between power transistors and mounting plate.
The junction temperature of silicon devices must be kept beneath about 150 ° C to avoid damage. Junction temperature, TJ, can be calculated from power dissipation, P, and the total thermal resistance, RJA - that is, the junction-to-ambient (air, environment) resistance - by the thermal analog of Ohm’s Law:
DT = P× Rthermal
where temperature drop is like voltage, power like current, and thermal resistance like electrical resistance. In particular, junction temperature can be calculated from:
where the thermal resistances (in order) are from junction to transistor case, case to heat-sink, and heat-sink to ambient temperature. TO-220 RJC is typically about 1 ° C/W and TO-204 packages are about a third to a fifth of that. Heat-sink thermal resistances are given in heat-sink data sheets and vary greatly with air flow, which causes convective heat transfer. Otherwise, the contact of the metal transistor package with a metal heat-sink (often through a thermally but not electrically conducting insulating pad) allows conductive heat transfer. Thermal pads for TO-220 packages have typical thermal resistances of 1 degree C/W.