FET Channel - simplified representation of three terminal device called a field effect transistor (FET) - overall horizontal shape - current levels off as voltage increases - two regions of operation 1. triode: I = k(2v A V S - V S2 ) 0 < V S < V A 2. constant current: I = kv 2 A = I SS = constant V S >= V A where k = transconductance I SS = drain-source saturation current
FET Channel Biasing Figure 3.48 Load line of Thevenin circuit superimposed on the v-i characteristic of the FET channel - it is also possible to find solution mathematically if you assume correct region of operation
Given that we are in the constant current region: V TH - I R TH - V S = 0 V S = V TH - I R TH I = I SS = kv A 2 (0.5mA/V 2 )(4V) 2 = 8mA V S = 15V - (8mA)(1000Ω) = 15V - 8V = 7V What happens if we assume triode region? I = 2kV A V S - kv S 2 V S = V TH - 2kR TH V A V S - kr TH V S 2 kr TH V S 2 + (1 + 2kR TH V A )V - V TH = 0 Ax 2 + Bx + C = 0 x = -B B 2 ± - 4AC 2A
Current Regulation 1. If V T H increases to 20V V OC = 20V I SC = V TH /R TH = 20V/1KΩ = 20mA From graph I = I SS = 8mA 2. If R TH decreased to 750Ω V OC = 15V I SC = 15V/750Ω = 20mA From graph I = I SS = 8mA
Schottky iode - metallurgical junction of lightly doped semiconductor and metal (aluminum) Figure 3.32 Circuit symbol of Schottky diode - performs similar to PN junction diode and has similar V-I characteristics - turn-on voltage 0.3V - higher reverse saturation current - can switch from forward to reverse bias more quickly and introduces less noise than standard PN junction - commonly used in integrated circuits (IC s)
Varactor iode - when reverse biased a PN junction exhibits parasitic capacitance - in a varactor diode this property is enhanced to create a voltage controlled capacitor C = C 1+ -V 0 V V F = diode turn-on voltage - C can range from 2pF to 100pF - used in high frequency circuits - frequency modulation N = negative number -1/2 standard - voltage controlled oscillators (VCO s) F N (-1) --- (-4) varactor
Tunnel iode - heavily doped PN junction (much greater than zener) - depletion region becomes very narrow - quantum mechanical processed lead to interesting device behavior - central region has negative resistance - peak and valley parameters - high frequency oscillators
Metal Oxide Varistor (MOV) Figure 3.34 Circuit sykmbol and v-i characteristic of a typical metal oxide varistor (MOV) - functions like a zener for both positive and negative voltages - breakdown voltage can range from 15V to 1000V - breakdown time is short - commonly used for transient surge protection
Hall Effect - used to measure magnetic field strength - switches - when a magnet is brought near then ε exceeds some threshold Thermistor - conductivity increases by approx. 8% per o C - negative coefficient of resistance Metal has positive coefficient of resistance 0.4%/ o C Heavily doped semiconductor has positive coefficient of resistance - carrier mobility decreases with temp. - sensistor
LEs - recombination of holes and electrons results in emitted photons when diode is forward biased - spontaneous emission - incoherent light Laser - photon induces electron-hole recombination - stimulated emission - light is coherent (in phase) => laser beam - resonant cavity PIN - reverse bias - photons creates electron/hole pair
Additional Notes - hole/electron pairs going together: recombination - mobility => ease with which charged particles can move µ N = electron mobility µ P = hole mobility conductivity : σ = (nµ N + pµ P )e where : e = 1.602 X 10-19 coulombs n = free electron concentration p = hole concentration
For intrinsic semiconductor n = p = n i For extrinsic semiconductor n x p = n i 2 mass action law i.e.: doping for n definitely increases the number of electrons, but it decreases the number of holes onors electrons - majority carriers holes - minority carriers Acceptors holes - majority carriers electrons - minority carriers
Graphical solution - quick - easy to find - approximate - small number of devices Iterative mathematical solution - accurate - use successive iteration - large circuits (computer)
Figure 3.43 Flowchart of successive iteration method
η = 2 I S = 10nA room temp. V - I R - V = 0 TH TH I = V TH - V R TH T I = I (e -1) KVL S V / ηv I V = ηv T ln + 1 diode equation I S
Assume V = V = 0.7V F 1. I 6V - 0.7 5kΩ = 1.06mA 2. V 2(0.025V) ln 1.06mA 10nA + 1 = 0.5786V 3. I 6V - 0.5786V 5kΩ = 1.0843mA 4. V 2(0.025V) ln 1.0843mA + 1 10 na = 0.5797V 5. I 6V - 0.5797V 5kΩ = 1.0841mA 6. V 2(0.025V) ln 1.0843mA 10nA + 1 = 0.5797V (no change from step 4)
Figure 3.46 PN junction diode connected to resistive circuit containing an ac voltage source
Figure 3.47
- clipping circuits
Piecewise Linear Modeling - easy to use - accurate results - works with multiple elements - elements V-I characteristics as sequences of straight lines - straight lines can be represented as simple resistive circuits which operate over a limited region Figure 3.51 a) Resistive circuit with same v-i characteristic as the tangent line at point A; b) v-i characteristic of resistive circuit - model accurately in the vicinity of point A
Figure 3.50 Tangent to diode v-i characteristic at point A obeys the equation: v = V f + i r d
Sample question: etermine piecewise linear model for diode at I = 1mA, I S = 1nA - R = slope of diode V-I characteristic T I = I (e - 1) 1 R S = di dv V / ηv = IS V e V / η η V T T
- two lines segments usually sufficient to model diode - reverse bias --- horizontal line represented by open circuit - in elbow region the model is not accurate
Piecewise Model for AC Source - very good for small signal ac sources v = v 0 + v 1 sinωt - operating point is found with ac sources set to 0 - piecewise model is substituted for the given operating point
Space-charged Capacitances - width of insulator varied by changing reverse voltage - a capacitor with plates of metal and an insulator dielectric C α 1/d - change the reverse voltage and you change the capacitance - also referred to as : - transaction cap. - depletion cap. - barrier cap.
iffusion Capacitance - when diode is forward biased there exists another capacitance effect called diffusion capacitance, C C α 1/R where R is the dynamic (piecewise) resistance of the diode Junction iode Switching Times - going from reverse to forward bias there is some time to get to steady state. This is referred to as the forward recovery time T FR
Going from Forward to Reverse - don t get reverse potential until the injection of excess minority carriers have dropped to their normal value - after this the junction capacitance comes into effect and we get an RC time constant
Transfer Characteristics (Function) - functional relationship between inputs and outputs Figure 4.1 a) simple linear circuit Figure 4.1 b) voltage transfer characteristic
Transfer Characteristics (Function) (con t) -V + IR + IR = 0 dv dv IN 1 2 OUT IN I = V = IR = = OUT 2 R1 R + R 1 2 VIN (R + R ) 1 2 R2 R + R 1 2 = 1 K 2 K = 1 2 V IN
Limiter Circuit - multiple elements using piecewise linear model
Limiter Circuit (con t) -V + R I + R I + V = O V > V V = V + IR = V + dv dv IN 1 2 F IN F OUT F F OUT IN = R R + R 1 2 I = V IN - V R + R F 1 2 (V - V )R (R + R ) IN F 1 2 0 R << R 1 Figure 4.7 Transfer characteristic of the limiter circuit of Fig. 4.3
Modified Limiter Figure 4.9 Limiter circuit with voltage reference V R Figure 4.10 Piecewise linear model for forward-biased 1 and reversed biased 2 for the case v IN > (V R + V f )
Modified Limiter (con t) - V + IR + IR + V + V = 0 V > V + V IN 1 F R IN F R I = V IN - (V F + V R ) R + R 1 V = V + V + IR OUT R F = (V + V ) + Figure 4.11 Transfer characteristic of the circuit of Fig, 4.9 R F (V - (V + V ))R R + R IN R F 1
Zener Limiter Figure 4.13 Approximate piecewise linear models for three regions of zener operation: a) v IN > V f ; b) -V ZK < v IN < V f ; c) v IN < -V ZK
Zener Limiter (con t) Figure 4.12 Limiter circuit incorporating a zener diode Figure 4.14 Tranfer characteristic of the above circuit. This plot is similar to the of the two-diode limiting circuit of Fig. 4.7, with the turn-on voltage of 2 replaced by V ZK
Current Limiter 2 A S S Triode: I = k(2v V - V ), 1 R At I, V = 0 R = S S = di dv S 1 2kV = 500 Ω A = 2k(V - V ) A S Constant Current: I = kv = (25)(4) = 4mA 2 2 A
Current Limiter (con t) Figure 4.16 Tangent lines to be represented by piecewise linear models. Transition point from one line to the other occurs at i = 4mA, v S = 2V Figure 4.17 Circuit of Fig. 4.15 with a) triode region piecewise linear model, valid for v IN < 6V; b) constant current region piecewise linear model, valid for v IN > 6V
Rectifier Circuits - primary function is to change an ac input into a voltage which is only positive or negative Figure 4.19 Basic rectification function. The rectifier is assumed to be ideal
Half-wave Rectifier Figure 4.20 Basic half-wave positive rectifier incorporating a PN junction diode V - IR - V - IR = 0 IN F LOA I = V = OUT dv dv OUT IN V IN - V R + R = F LOA (V - V )R (R + R ) IN F LOA LOA RLOA (R + R ) Figure 4.22 Transfer characteristic of the half-wave rectifier circuit of Fig. 4.20 with rd assumed negligibly small LOA 1
Accuracy of Piecewise Model Figure 4.23 Load voltage and current vs time for the half-wave rectifier circuit of Fig.4.20 Assume R R + R LOA LOA = 1 V = OUT (V IN - V F) (R + R ) LOA R = ηv I (from previous analysis) T
Accuracy of Piecewise Model (con t) At V = 5.7V IN At V = 1 IN I = V IN - V R LOA F 5.7V - 0.7V = 1000Ω = 5 ma I = V IN - V R LOA F 1V - 0.7V = 1000Ω = 0.3mA R = (2)(0.025v) 5mA = 10Ω R = (2)(0.025) 0.3mA = 167 Ω R R + R LOA LOA = 1000 1010 = 0.99 R R + R LOA LOA = 1000 1167 = 0.86 V = 4.95V not 5V OUT V = 0.26V not 0.3V OUT
Bridge Rectifier Figure 4.28 Bridge rectifier circuit with arbitrary passive load
Bridge Rectifier (con t) - many important applications - current flows through the load for both the positive and the negative values of V IN - V IN > 2V F Figure 4.29 Current flow path for the case v IN > 2V f
Figure 4.31 Input-output voltage transfer characteristic of the bridge rectifier of Fig. 4.28 Figure 4.30 Current path for case v IN < -2V f
Figure 4.32 Load versus time for triangle-wave input of 10V peak. A value of V f = 0.6V has been assumed
Power Supply Circuits - accept voltage as input and provide a C voltage as its output - used to power other electronic circuits - heart of every power supply is a rectifier circuit Half-wave Rectifier Power Supply - crude power supply - half-wave rectifier and capacitor Figure 4.34 Half -wave rectifier with capacitor and load connected to the v OUT terminals
Figure 4.35 Capacitor voltage vs. time for the power supply of Fig. 4.34 when the load is a resistor of value R L. In a well-designed supply, the decay of the capacitor, which begins at point A and ends at point B, is small compared to V P V C (t) = (V P - V F )e -t/r L C where: V P = Peak Voltage Ripple = V P - V C (min) Large C => small ripple Large R L => small ripple
Example 4.5 - estimate ripple - V = (V - V ) e C P C - for sinwave: V = 2 V = 2 (12V) - V 0.6V V - V = 16.4V -t/r C = 17V t = T = 1 1 MAX = = 0.0167s = 16.7ms f 60Hz R C = (200 Ω )(1000µ F) L F P F = 200000 x 10-6s = 200ms V = 16.4 e - (16.7 / 200) = 15.1V C V = 16.4V - 15.1V = 1.3V RIPPLE P L RMS
Full Wave Rectifier Power Supply - minimize load under load conditions - full wave rectifier gives 1/2 the ripple for the same value of capacitance - also uses negative portions of ac input to recharge capacitor - typically uses bridge for center-tapped rectifier - driven from secondary windings of transformer Figure 4.37 Full-wave, center-tapped rectifier power supply circuit
Figure 4.38 Capacitor is charged positively through alternate halves of the full wave rectifier. The input voltage v IN is multiplied by the transformer turns ratio and applied across each of the secondary windings Top: current path for positive v IN ; Bottom: current path for negative v IN
- the senses or polarity of both secondary windings is in the same direction - capacitor decays for only half the period of the sinusoid Figure 4.39 Full-wave bridge rectifier power supply circuit
Voltage Regulation Power supply => transformer, rectifier, cap. filter, voltage regulator - further reduces ripple component - usually integrated circuit - active device with terminals: input, output, common - generates near constant voltage with negligible ripple - input voltage needs to be greater than output voltage Figure 4.40 Integrated circuit voltage regulator connected to a bridge rectifier power supply
- simple regulator can be made with resistor and zener diode Figure 4.41 Zener regulated power supply - zener must remain in reverse breakdown at all times - bias so that a minimum of 1 ma flows through zener when capacitor voltage V C is at minimum