Chapter #4: Diodes from Microelectronic Circuits Text by Sedra and Smith Oxford Publishing Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) IntroducLon § IN THIS CHAPTER WE WILL LEARN § the characteris:cs of the ideal diode and how to analyze and design circuits containing mul:ple ideal diodes together with resistors and dc sources to realize useful and interes:ng nonlinear func:on § the details of the i-­‐v characteris:c of the junc:on diode (which was derived in Chapter 3) and how to use it to analyze diode circuits opera:ng in the various bias regions: forward, reverse, and breakdown § a simple but effec:ve model of the diode i-­‐v characteris:c in the forward direc:on: the constant-­‐voltage-­‐drop model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) IntroducLon § a powerful technique for the applica:on and modeling of the diode (and in later chapters, transistors): dc-­‐biasing the diode and modeling its opera:on for small signals around the dc-­‐opera:ng point by means of the small-­‐signal model § the use of a string of forward-­‐biased diodes and of diodes opera:ng in the breakdown region (zener diodes), to provide constant dc voltages (voltage regulators) § applica:on of the diode in the design of rec:fier circuits, which convert ac voltages to dc as needed for powering electronic equipment § a number of other prac:cal and important applica:ons Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.1.1. Current-­‐Voltage CharacterisLc of the Ideal Diode § ideal diode – most fundament nonlinear circuit element § two terminal device § circuit symbol shown to right § operates in two modes § on and off Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.1: Diode characteris:cs 4.1.1. Current-­‐Voltage CharacterisLc § cathode – nega:ve terminal, from which current flows § anode – posi:ve terminal of diode, into which current flows § voltage-­‐current (VI) behavior is: § piecewise linear for rated values § nonlinear beyond this range Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.1.1: Current-­‐Voltage Characteris:c of the Ideal Diode mode #2: reverse bias = open ckt. § ideal diode: is most fundament device scircuit ymbol nonlinear element with two nodes § two terminal device with circuit symbol to right § operates in two modes forward and reverse bias mode #1: forward bias = short ckt figure 4.1. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.1.1. Current-­‐
Voltage CharacterisLc § External circuit should be designed to limit… § current flow across conduc:ng diode § voltage across blocking diode Figure 4.2: The two modes of § Examples are shown to opera:on of ideal diodes and the right… use of an external circuit to limit Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) (a) the forward current and (b) the reverse voltage. 4.1.2: A Simple ApplicaLon – The RecLfier § One fundamental applica:on of this piecewise linear behavior is the rec:fier. § Q: What is a recLfier? § A: Circuit which converts AC waves in to DC…ideally with no loss. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.3(a): Rec:fier Circuit 4.1.2: A Simple ApplicaLon – The RecLfier § This circuit is composed of diode and series resistor. § Q: How does this circuit operate? § A: The diode blocks reverse current flow, preven:ng nega:ve voltage across R. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.3(a): Rec:fier Circuit Example 4.1: Diode Rec:fier § Consider the circuit of Figure 4.4. A source (vS) with peak amplitude of 24V is employed to charge a 12V dc-­‐ba\ery. § Q(a): Find the frac:on of each cycle during which the diode conducts. § Q(b): Find peak value of diode current and maximum reverse-­‐bias voltage that appears across the diode. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.4: Circuit and Waveforms for Example 4.1. 4.1.3. Another ApplicaLon, Diode Logic Gates § Q: How may diodes be used to create logic gates? § A: Examples of AND / OR gates are shown right. § Refer to next slide. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.5: Diode logic gates: (a) OR gate; (b) AND gate (in a posi:ve-­‐logic system). OR GATE AND GATE IF vA = 5V THEN diodeA will conduct AND vY = vA = 5V IF vA = 0V THEN diodeA will conduct AND vY = vA = 0V IF all diodes block THEN vY = 5V + 5V
-­‐ IF any diode conducts Oxford University Publishing THEN vbYy A=del 5S. SV Microelectronic Circuits edra and Kenneth C. Smith (0195323033) + 5V -­‐ Example 4.2: More Diodes
To apply nodal / mesh techniques, one must have knowledge of all component impedances. Figure 4.4: Circuit and Waveforms for Example 4.1. § Q: What difficul:es are associated with mul:-­‐diode circuits? § A: Circuit cannot be solved without knowledge of diodes’ statuses. Yet, statuses are dependent on the Figure 4.6: Circuits for Example 4.2. solu:on. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) IF vB < 0 THEN ZD1 = 0ohms ELSE ZD1 = open circuit Example 4.2: More Diodes
§ Q: How does one solve these circuits? § A: One must use the following steps… § 1) assume the status of all diodes § 2) solve via mesh / nodal analysis § 3) check for coherence Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Example 4.2: If answer to either of these is no, More Diodes then the solu:on is not physically realizable. § Q: How does one check for coherence? § A: One must ask the following ques:ons… § 1) Are calculated voltages across all “assumed conduc:ng” diodes forward-­‐biased? § 2) Are the calculated currents through all “assumed blocking” diodes zero? § Q: What does one do, if the solu:on is not coherent? § A: One must change one or more of these assump:ons and solve as well as check for coherence again. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.2. Terminal CharacterisLcs of JuncLon Diodes § Most common implementa:on of a diode u:lizes pn junc:on. § I-­‐V curve consists of three characteris:c regions § forward bias: v > 0 § reverse bias: v < 0 § breakdown: v << 0 Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) discon:nuity caused by differences in scale 4.2.1. The Forward-­‐Bias Region IS =!constant!for!diode!at!given
temperature!(aka.!saturation!current)
§ The forward-­‐bias region of opera:on is entered when v > 0. § I-­‐V rela:onship is closely approximated by equa:ons to right. (4.3) is a simplifica:on suitable for large v Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) !###"###$
v/VT
(eq4.1)(i = IS (e −1)
VT =!thermal!voltage
k=!Boltzmann's!constant!(8.62E!5#eV/K)
q=!magnitude!of!electron!charge!(1.6E!19$C)
!####"####$
kT
(eq4.2)!VT = =
25.8mV
%#
&#
'
q at#room
temperature
IS =!constant!for!diode!at!given
temperature!(aka.!saturation!current)
!##"##$
v/V
(eq4.3)$i = IS e T
4.2.1. The Forward-­‐Bias Region § Equa:on (4.3) may be reversed to yield (4.4). § This rela:onship applies over as many as seven decades of current. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) IS =!constant!for!diode!at!given
temperature!(aka.!saturation!current)
!###"###
$
!i$
(eq4.4)'v =VT ln## &&
" IS %
4.2.1. The Forward-­‐Bias Region § Q: What is the rela:ve effect of current flow (i) on forward biasing voltage (v)? § A: Very small. § 10x change in i, effects 60mV change in v. step%#1:%consider%two%cases%(#1%and%#2)
!
####"####$
V1 /VT
V2 /VT
I1 = IS e !and!!I2 = IS e
step%#2:%divide%I2 "by"I1
!#"#$
V2 /VT
I2 IS e
= V /V
I1 IS e 1 T
step%#3:%combine%two%exponentials
!#"#$
I2
(V −V )/V
=e 2 1 T
I1
step%#4:%invert%this%expression
!
##
#"###
$
V2 −V1 =VT ln I2 / I1
(
)
step%#5:%convert%to%log%base%10
!###
#"####
$
V2 −V1 = 2.3VT log I2 / I1
%##&##
'
60mV ≈2.3VT log(10/1)
(
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) )
4.2.1: The Forward-­‐Bias Region § cut-­‐in voltage – is voltage, below which, minimal current flows § approximately 0.5V § fully conducLng region – is region in which Rdiode is approximately equal 0 § between 0.6 and 0.8V Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) fully conduc:ng region Example 4.3 § Refer to textbook… Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.2.2. The Reverse-­‐
Bias Region § The reverse-­‐bias region of opera:on is entered when v < 0. § I-­‐V rela:onship, for nega:ve voltages with |
v| > VT (25mV), is closely approximated by equa:ons to right. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) this&expression
applies&for
negative&voltages
!#"#$
i = −IS e
− v /VT
action:!invert!exponential
!#
#"##
$
" 1 %
i = −IS $$ v /V ''
#!"#
e T&
≈0$for$larger
voltage
magnitudes
i = −IS
4.2.2. The Reverse-­‐
Bias Region § A “real” diode exhibits reverse-­‐bias current, although small, much larger than IS . § 10-­‐9 vs. 10-­‐14Amps § A large part of this reverse current is a\ributed to leakage effects. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.2.3. The Breakdown Region § The breakdown region of opera:on is entered when v < VZK. § Zener-­‐Knee Voltage (VZK) § This is normally non-­‐
destruc:ve. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) breakdown region i = IS (e
− 1)
i = −IS
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) i = IS e
V = 10VT V = -­‐VT V = -­‐VZK i << −IS
v / VT
− v / VT
4.3. Modeling the Diode Forward CharacterisLc § The previous slides define a robust set of diode models. § Upcoming slides, however, discuss simplified diode models be\er suited for use in circuit analyses: § exponen:al model § constant voltage-­‐drop model § ideal diode model § small-­‐signal (lineariza:on) model Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.1. The ExponenLal Model § exponenLal diode model § most accurate § most difficult to employ in circuit analysis § due to nonlinear nature V /V
(eq4.6)((ID = IS e D T
!##
#"###
$
VD =!voltage!across!diode
ID =!current!through!diode
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.1. The ExponenLal Model § Q: How does one solve for ID in circuit to right? § VDD = 5V § R = 1kOhm § ID = 1mA @ 0.7V § A: Two methods exist… § graphical method § iteraLve method Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.10: A simple circuit used to illustrate the analysis of circuits in which the diode is forward conduc:ng. VDD − VD
(eq4.7) ID =
R
4.3.2. Graphical Analysis Using ExponenLal Model § step #1: Plot the rela:onships of (4.6) and (4.7) on single graph § step #2: Find intersec:on of the two… § load line and diode characteris:c intersect Figure 4.11: Graphical analysis of the circuit in Fig. 4.10 using the at operaLng point exponen:al diode model. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.2. Graphical Analysis Using ExponenLal Model § Pro’s § Intui:ve § b/c of visual nature § Con’s § Poor Precision § Not Prac:cal for Complex Analyses § mul:ple lines required Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.11: Graphical analysis of the circuit in Fig. 4.10 using the exponen:al diode model. 4.3.3. IteraLve Analysis Using ExponenLal Method § step #1: Start with ini:al § step #4: Repeat these guess of VD. steps un:l VD(k+1) = VD(k). § VD(0) § Upon convergence, the new and old values of § step #2: Use nodal / mesh VD will match. analysis to solve ID. § step #3: Use exponen:al model to update VD. § VD(1) = f(VD(0)) Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.3. IteraLve Analysis Using ExponenLal Method § Pro’s § High Precision § Con’s § Not Intui:ve § Not Prac:cal for Complex Analyses § 10+ itera:ons may be required Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3. Modeling the Diode Forward CharacterisLc § Q: How can one analyze these diode-­‐based circuits more efficiently? § A: Find a simpler model. § One example is assume that voltage drop across the diode is constant. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.5. The Constant Voltage-­‐
Drop Model § The constant voltage-­‐
drop diode model assumes that the slope of ID vs. VD is ver:cal @ 0.7V § Q: How does example 4.4 solu:on change if CVDM is used? § A: 4.262mA to 4.3mA Figure 4.12: Development of the Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) diode constant-­‐voltage-­‐drop model: (a) the… 4.3.6. Ideal Diode Model § The ideal diode model assumes that the slope of ID vs. VD is ver:cal @ 0V § Q: How does example 4.4 solu:on change if ideal model is used? § A: 4.262mA to 5mA Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.1.1: Current-­‐Voltage Characteris:c of the Ideal Diode mode #2: reverse bias = open ckt. § ideal diode: is most fundament device scircuit ymbol nonlinear element with two nodes § two terminal device with circuit symbol to right § operates in two modes forward and reverse bias mode #1: forward bias = short ckt figure 4.1. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) When to use these models? § exponenLal model § low voltages § less complex circuits § emphasis on accuracy over prac:cality § constant voltage-­‐drop mode: § medium voltages = 0.7V § more complex circuits § emphasis on prac:cality over accuracy Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) § ideal diode model § high voltages >> 0.7V § very complex circuits § cases where a difference in voltage by 0.7V is negligible § small-­‐signal model § this is next… 4.3.7. Small-­‐Signal Model § small-­‐signal diode model § Diode is modeled as variable resistor. § Whose value is defined via lineariza:on of exponen:al model. § Around bias point defined by constant voltage drop model. § VD(0) = 0.7V Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.7. Small-­‐Signal Model Neither of these circuits employ the exponen:al model – simplifying the “solving” process. § Q: How is the small-­‐signal diode model defined? § A: The total instantaneous circuit is divided into steady-­‐state and :me varying components, which may be analyzed separately and solved via algebra. § In steady-­‐state, diode represented as CVDM. § In :me-­‐varying, diode represented as resistor. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) CVDM DC Total Instantaneous AC (vD.) Solu:on =
DC Steady-­‐State Solu:on (VD.) +
Time-­‐Varying AC Solu:on (vd.) Figure 4.14: (a) C ircuit for Example 4.5. (b) Circuit for calcula:ng the Oxford University Publishing point. c) Small-­‐signal equivalent circuit. Microelectronic Cdc ircuits o
by pera:ng Adel S. Sedra and Kenneth C. Smith ((
0195323033) 4.3.7. Small-­‐Signal Model § Q: How is the small-­‐signal diode model defined? § step #1: Consider the conceptual circuit of Figure 4.13(a). § DC voltage (VD) is applied to diode § Upon VD, arbitrary :me-­‐varying signal vd is super-­‐imposed Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.7. Small-­‐Signal Model § DC only – upper-­‐case w/ upper-­‐
case subscript § Lme-­‐varying only – lower-­‐case w/ lower-­‐case subscript § total instantaneous – lower-­‐case w/ upper-­‐case subscript § DC + :me-­‐varying Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.3.7. Small-­‐Signal Model § step #2: Define DC current as in (4.8). § step #3: Define total instantaneous voltage (vD) as composed of VD and vd. § step #4: Define total instantaneous current (iD) as func:on of vD. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) V /VT
(eq4.8)((ID = IS e D
(eq4.9)(( vD (t) =VD +vd (t)
!##"##$
vD (t)=!total!instantaneous
!!!!!voltage!across!diode
VD =!dc!component
!!!!!of!vD (t)
vd (t)=!time!varying
!!!!!component!of!vD (t)
v /V
(eq4.10))) iD (t) = IS e D T
!#
#"##
$
note%that%this%is
different%from%(4.8)
4.3.7. Small-­‐Signal Model § step #5: Redefine (4.10) as func:on of both VD and vd. § step #6: Split this exponen:al in two. § step #7: Redefine total instant current in terms of DC component (ID) and :me-­‐varying voltage (vd). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) VD +vd )/VT
(
(eq4.11)((iD (t) = IS e
action:!split!this!exponential
using!appropriate!laws
!##
#"###
$
V /V
v /V
(eq4.11))) iD (t) = IS e D T e d T
!"#
ID
v /VT
(eq4.12)))iD (t) = ID e D
4.3.7. Small-­‐Signal Model § step #8: Apply power series expansion to (4.12). § step #9: Because vd/
VT << 1, certain terms may be neglected. x2 x3 x 4
example:((e = 1+ x + + + +…
2! 3! 4!
x
action:!apply!power!series!expansion!to!(4.12)!
!#######
#"########
$
because*vd /VT <<1,#these#terms
!
$
are#assumed#to#be#negligible
#
!####"####$ &
#
&
'! $2 * '! $3 *
v
v
v
1
1
#
&
(eq4.12a)"" iD (t) = ID #1+ d + )## d && , + )## d && , +…&
VT )" VT % 2!, )" VT % 3!,
#
&
(
+ (
+
##
&&
"%######&######'%
power#series#expansion#of#e
action:!eliminate
negligible!terms!
!##"##$
! v $
(eq4.14)!! iD (t) = ID ##1+ d &&
" VT %
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) vd /VT
4.3.7. Small-­‐Signal Model § small signal approximaLon § Shown to right for exponen:al diode model. § total instant current (iD) § small-­‐signal current (id.) § small-­‐signal resistance (rd.) § Valid for for vd < 5mV amplitude (not peak to peak). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) !I $
iD (t) = ID + ## D &&vd
VT %
"!"#
id
iD (t) = ID + id
1
id = v d
rd
rd =
VT
ID
4.3.7. Small-­‐Signal Model § This method may be used to approximate any func:on y = f(x) around an opera:ng point (x0, y0). ! ∂y
y(t) = y0 + #
# ∂x
"
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) −1
Δx #
$
$ !#"
& x(t)− x
0
&
y=Y %
(
)
4.3.7: Small-­‐Signal Model § Q: How is small-­‐signal resistance rd defined? § A: From steady-­‐state current (ID) and thermal voltage (VT) as below. § Note this approxima:on is only valid for small-­‐
signal voltages vd < 5mV. VT
rd =
ID
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Example 4.5: Small-­‐Signal Model § Consider the circuit shown in Figure 4.14(a) for the case in which R = 10kOhm. § The power supply V+ has a dc value of 10V over which is super-­‐imposed a 60Hz sinusoid of 1V peak amplitude (known as the supply ripple) § Q: Calculate both amplitude of the sine-­‐wave signal observed across the diode. § A: vd.(peak) = 2.68mV § Assume diode to have 0.7V drop at 1mA current. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.14: (a) c ircuit for Example 4.5. (b) circuit for calcula:ng the Oxford University Publishing pera:ng point. c) small-­‐signal equivalent circuit. Microelectronic Cdc ircuits o
by A
del S. Sedra and Kenneth C. Smith ((
0195323033) 4.3.8. Use of Diode Forward Drop in Voltage RegulaLon § Q: What is a voltage § Q: What characteris:c of regulator? the diode facilitates voltage regula:on? § A: Circuit whose § A: The approximately voltage output remains stable in spite of constant voltage drop changes in supply and across it (0.7V). load. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Example 4.6: Diode-­‐Based Voltage Regulator § Consider circuit shown in Figure 4.15. A string of three diodes is used to provide a constant voltage of 2.1V. § Q: What is the change in this regulated voltage caused by (a) a +/-­‐ 10% change in supply voltage and (b) connec:on of 1kOhm load resistor. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.15: Circuit for Example 4.6. ny means without the publisher's prior permission. Use (other than qualified fair use) in violation of the law or Terms of
osecuted to the full extent of the law.
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.4. OperaLon in the Reverse Breakdown Region – Zener Diodes § Under certain circumstances, diodes may be inten:onally used in the reverse breakdown region. § These are referred to as Zener Diodes. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) prosecuted to the full extent of the law.
Example 4.7 Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Example 4.7 (cont.) Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Prob. 4-­‐56 Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Prob. 4-­‐56 (cont.) Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5. RecLfier Circuits § One important applica:on of diode is the recLfier – § Electrical device which converts alterna:ng current (AC) to direct current (DC) § One important applica:on of rec:fier is dc power supply. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.20: Block diagram of a dc power supply step #1: increase / decrease rms magnitude of AC wave via power transformer step #2: convert full-­‐wave AC to half-­‐wave DC (s:ll :me-­‐varying and periodic) step #3: employ low-­‐pass filter to reduce wave amplitude by > 90% step #4: employ voltage regulator to eliminate ripple step #5: supply dc load . Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.20: Block diagram of a dc power supply 4.5.1. The Half-­‐
Wave RecLfier § half-­‐wave recLfier – u:lizes only alternate half-­‐cycles of the input sinusoid § Constant voltage drop diode model is employed. Figure 4.21: (a) Half-­‐wave rec:fier (b) Transfer characteris:c of the Oxford University Publishing rec:fier circuit (c) Input and output waveforms Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.1. The Half-­‐
Wave RecLfier § current-­‐handling capability – what is maximum forward current diode is expected to conduct? § peak inverse voltage (PIV) – what is maximum reverse voltage it is expected to block w/o breakdown? Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.1. The Half-­‐
Wave RecLfier § exponenLal model? It is possible to use the diode exponen:al model in describing rec:fier opera:on; however, this requires too much work. § small inputs? Regardless of the model employed, one should note that the rec:fier will not operate properly when input voltage is small (< 1V). § Those cases require a precision recLfier. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.2. The Full-­‐Wave RecLfier § Q: How does full-­‐wave rec:fier differ from half-­‐wave? § A: It u:lizes both halves of the input § One poten:al is shown to right. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.22: Full-­‐wave rec:fier u:lizing a transformer with a center-­‐tapped secondary winding. The key here is center-­‐tapping of the transformer, allowing “reversal” of certain currents… Figure 4.22: full-­‐wave rec:fier u:lizing a transformer with a center-­‐
tapped secondary winding: (a) circuit; (b) transfer characteris:c assuming a constant-­‐voltage-­‐drop model for the diodes; (c) input Oxford University Publishing and utput waveforms. Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith o
(0195323033) When instantaneous source voltage is posiLve, D1 conducts while D2 blocks… Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) when instantaneous source voltage is negaLve, D2 conducts while D1 blocks Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.2. The Full-­‐Wave RecLfier § Q: What are most important observa:on(s) from this opera:on? § A: The direc:on of current flowing across load never changes (both halves of AC wave are rec:fied). The full-­‐wave rec:fier produces a more “energe:c” waveform than half-­‐wave. § PIV for full-­‐wave = 2VS – VD Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.3. The Bridge RecLfier § An alterna:ve implementa:on of the full-­‐wave rec:fier is bridge recLfier. § Shown to right. Figure 4.23: The bridge rec:fier circuit. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) when instantaneous source voltage is posiLve, D1 and D2 conduct while D3 and D4 block Figure 4.23: The bridge rec:fier circuit. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) when instantaneous source voltage is posiLve, D1 and D2 conduct while D3 and D4 block Figure 4.23: The bridge rec:fier circuit. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.3: The Bridge RecLfier (BR) § Q: What is the main advantage of BR? § A: No need for center-­‐tapped transformer. § Q: What is main disadvantage? § A: Series connec:on of TWO diodes will reduce output voltage. § PIV = VS – VD Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § Pulsa:ng nature of rec:fier output makes unreliable dc supply. § As such, a filter capacitor is employed to remove ripple. Figure 4.24: (a) A simple circuit used to illustrate the effect of a filter capacitor. (b) input and output waveforms assuming an ideal Oxford University Publishing diode. Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § step #1: source voltage is posi:ve, diode is forward biased, capacitor charges. § step #2: source voltage is reverse, diode is reverse-­‐
biased (blocking), capacitor cannot discharge. § step #3: source voltage is posi:ve, diode is forward biased, capacitor charges (maintains voltage). Figure Oxford 4.24 ( a) Publishing A simple circuit used to illustrate the effect… University Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § Q: Why is this example unrealis:c? § A: Because for any prac:cal applica:on, the converter would supply a load (which in turn provides a path for capacitor discharging). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § Q: What happens when load resistor is placed in series with capacitor? § A: One must now consider the discharging of capacitor across load. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § The textbook outlines how Laplace Transform may be used to define behavior below. circuit state #1 output%voltage%for%state%#1
!
##"##$
vO t = vI t −vD
() ()
v (t ) =V e
%##&##'
−
O
peak
t
RC
output%voltage%for%state%#2
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) circuit state #2 Q: What happens when load resistor is placed in series with capacitor? § step #1: Analyze circuit state #1. § When diode is forward biased and conduc:ng. § step #2: Input voltage (vI) will be applied to output (vO), minus 0.7V drop across diode. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) circuit state #1 vO
iL =
R
iD = iC + iL
action: define capacitor
current differentially
6 44 7 4 48
dvI
iD = C
+ iL
dt
Q: What happens when load resistor is placed in series with capacitor? § step #3: Define output voltage for state #1. output%voltage%for%state%#1
!#"#$
vO = vI −vD
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) circuit state #1 Q: What happens when load resistor is placed in series with capacitor? § step #4: Analyze circuit state #2. § When diode is blocking and capacitor is discharging. § step #5: Define KVL and KCL for this circuit. § vO = RiL § iL = –iC Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) circuit state #2 Q: What happens when load resistor is placed in series with capacitor? § step #6: Use combina:on of circuit and Laplace Analysis to solve for vO(t) in terms of ini:al condi:on and :me… Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor vO = RiL
action:"replace
iL !with!&iC
!
#"#
$
vO = −RiC
action:"define"iC
differentially
action:"take"Laplace"transform
!
##
#"###
$
(*
,*
dvO
L )vO + RC
= 0dt
*+
*.
action:"take"Laplace"transform
!####
#"#####
$
VO s + RC /0sVO s −VO 0 12 = 0
%##&##'
()
() ()
!##"##$
transform)of)
dt
" dv % action:"seperate"disalike"/"collect"alike"terms
#"#####
$
vO = −R $$C O '' !####
dt & V s + RCsV s = RCV 0
#%&
O
O
O
# #
' %
!
##
&
##
'
iC
initial
(1+RCs)VO (s)
condition
action:"change"sides
!##"##
$
action:"pull"out"RC
!###
#"####
$
dvO
vO + RC
= 0 1+ RCs V s = RCV 0
O
O
dt
%##&##
'
dvO
()
(
()
) ()
" 1 %
RC $$ s+ ''VO (s)
Oxford University Publishing # RC &
Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) ()
()
action:"eliminate"RC !from!both!sides
!####
#"#####
$
"
1 %
RC $ s + 'VO s = RCVO 0
# RC &
action:"solve"for"VO ( s )
!###"###
$
()
()
()
VO s =VO 0
()
1
1
RC
action:"take"inverse"Laplace
!####
#"#####
$
(
,
*
*
1
L−1 )VO s =VO 0
s +1 / RC *.
*+
action:"solve
!###
"###$
()
()
s+
()
()
vO t =VO 0 e
−
( )
t
RC
4.5.4. The RecLfier with a Filter Capacitor § Q: What is VO(0)? § A: Peak of vI, because the transi:on between state #1 and state #2 (aka. diode begins blocking) approximately as vI drops below vC. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § step #7: Define output voltage for states #1 and #2. circuit state #1 output%voltage%for%state%#1
!
##"##$
vO t = vI t −vD
() ()
v (t ) =V e
%##&##'
−
O
peak
t
RC
output%voltage%for%state%#2
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) circuit state #2 output%voltage%for%state%#1
!#"#$
vO t = v I t
() ()
v (t ) =V e
%##&##'
−
O
peak
t
RC
output%voltage%for%state%#2
Figure 4.25: Voltage and Current Waveforms in the Peak Rec:fier Circuit W
ITH RC >> T. The diode is assumed ideal. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) A Couple of ObservaLons § The diode conducts for a brief interval (Δt) near the peak of the input sinusoid and supplies the capacitor with charge equal to that lost during the much longer discharge interval. The la\er is approximately equal to T. § Assuming an ideal diode, the diode conduc:on begins at :me t1 (at which the input vI equals the exponen:ally decaying output vO). Diode conduc:on stops at :me t2 shortly auer the peak of vI (the exact value of t2 is determined by se\ling of ID). Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) A Couple of ObservaLons § During the diode off-­‐interval, the capacitor C discharges through R causing an exponen:al decay in the output voltage (vO). At the end of the discharge interval, which lasts for almost the en:re period T, voltage output is defined as follows – vO(T) = Vpeak – Vr. § When the ripple voltage (Vr) is small, the output (vO) is almost constant and equal to the peak of the input (vI). the average output voltage may be defined as below… (eq4.27) avg (VO ) = Vpeak
1
− Vr ≈ Vpeak if Vr is small
2
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor ()
vO t =Vpeak e
§ Q: How is ripple voltage (Vr) defined? § step #1: Begin with transient response of output during “off interval.” § step #2: Note T is discharge interval. § step #3: Simplify using assump:on that RC >> T. § step #4: Solve for ripple voltage Vr. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) −
t
RC
T !is!discharge!interval
!
##"##$
Vpeak −Vr = vO (T)
$ −T '
Vpeak −Vr ≈ Vpeak × && e RC ))
%!(
because'RC>>T ,
we$can$assume...
T
−
T
RC
e
!≈!1−
RC
action:"solve"for
ripple"voltage"Vr
!##"##
$
$T '
(eq4.28)))Vr ≈ Vpeak & )
RC (
%!
1−
T
−1
RC
4.5.4. The RecLfier with a Filter Capacitor § step #5: Put expression in terms of frequency (f = 1/T). Vpeak
§ Observe that, as long as Vr }R
Vpeak
IL
<< Vpeak, the capacitor (eq4.29) Vr ≈
=
discharges as constant fRC
fC
current source (IL). § Q: How is conducLon interval (Δt) defined? expression to define § A: See following slides… Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) ripple voltage (Vr) cos(0O) Q: How is conducLon interval (Δt) defined? § step #1: Assume that diode conduc:on stops (very close to when) vI approaches its peak. § step #2: With this assump:on, one may define expression to the right. § step #3: Solve for ωΔt. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) ( )
Vpeak cos ωΔt =Vpeak −Vr
!####"####
$
note%that%peak%of%vI%represents%cos(0O ),
therefore%cos ωΔt !represents!variation
around!this!value!
( )
(eq4.30)!! ωΔt = 2Vr /Vpeak
!##
#"###
$
as#assumed,#conduction
interval#Δt !will!be!small
when!Vr <<Vpeak
4.5.4. The RecLfier with a Filter Capacitor Vpeak
!R
§ Q: How is peak-­‐to-­‐peak Vpeak IL
ripple (Vr) defined? (eq4.29)))Vr ≈
=
fRC fC
§ A: (4.29) § Q: How is the conduc:on interval (Δt) defined? (eq4.30))) ωΔt = 2Vr /Vpeak
!##
#"###
$
§ A: (4.30) as#assumed,#conduction
interval#Δt !will!be!small
when!Vr <<Vpeak
Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.5.4. The RecLfier with a Filter Capacitor § precision recLfier – is a device which facilitates rec:fica:on of low-­‐voltage input waveforms. Figure 4.27: The “Superdiode” Precision Half-­‐Wave Rec:fier and Oxford University Publishing its almost-­‐ideal transfer characteris:c. Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.6: LimiLng and Clamping Circuits § Q: What is a limiter circuit? § A: One which limits voltage output. Figure 4.28: General transfer characteris:c for a limiter circuit Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 4.6. LimiLng and Clamping Circuits § passive limiter circuit § has linear range § has nonlinear range § K < 1 § examples include § single limiter operate in uni-­‐polar manner § double limiter operate in bi-­‐polar manner Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) !
over%linear%range
!
#
#
KvI
vO = "
# constant'value(s)
!##"###
$
#$
outside'linear'range
!
# L
# −
##
vO = " KvI
#
#
# L+
#$
vI ≤
L!
K
L−
K
< vI <
vI ≥
L+
K
L+
K
4.6. LimiLng and Clamping Circuits § sou vs. hard limiter Figure 4.30: H ard vs. Sou Oxford University Publishing Microelectronic Circuits by Limi:ng. Adel S. Sedra and Kenneth C. Smith (0195323033) § Q: How are limiter circuits applied? § A: Signal processing, used to prevent breakdown of transistors within various devices. single limiters employ one diode double limiters employ two diodes of opposite polarity linear range may be controlled via string of diodes and dc sources zener diodes may be used to implement sou limi:ng Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.31: Variety of basic limi:ng circuits. 4.6.2. The Clamped Capacitor or DC Restorer § Q: What is a dc restorer? § A: Circuit which removes the dc component of an AC wave. § Q: Why is this ability important? § A: Average value of this output (w/ dc = 0) is effec:ve way to measure duty cycle Figure 4.32: The clamped Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) capacitor or dc restorer with a square-­‐wave input and no load 4.6.3: The Voltage Doubler § Q: What is a voltage doubler? § A: One which mul:plies the amplitude of a wave or signal by two. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Figure 4.34: Voltage doubler: (a) circuit; (b) waveform of the voltage across D1. Summary (1) § In the forward direc:on, the ideal diode conducts any current forced by the external circuit while displaying a zero-­‐voltage drop. The ideal diode does not conduct in reverse direc:on; any applied voltage appears as reverse bias across the diode. § The unidirec:onal current flow property makes the diode useful in the design of rec:fier circuits. § The forward conduc:on of prac:cal silicon-­‐junc:on diodes is accurately characterized by the rela:onship i = ISeV/VT. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary (2) § A silicon diode conducts a negligible current un:l the forward voltage is at least 0.5V. Then, the current increases rapidly with the voltage drop increasing by 60mV for every decade of current change. § In the reverse direc:on, a silicon diode conducts a current on the order of 10-­‐9A. This current is much greater than IS and increases with the magnitude of reverse voltage. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary (3) § Beyond a certain value of reverse voltage (that depends on the diode itself), breakdown occurs and current increases rapidly with a small corresponding increase in voltage. § Diodes designed to operate in the breakdown region are called zener diodes. They are employed in the design of voltage regulators whose func:on is to provide a constant dc voltage that varies li\le with varia:ons in power supply voltage and / or load current. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary (4) § In many applica:ons, a conduc:ng diode is modeled as having a constant voltage drop – usually with value of approximately 0.7V. § A diode biased to operate at a dc current ID has small signal resistance rd = VT/ID. § Rec:fiers covert ac voltage into unipolar voltages. Half-­‐
wave rec:fiers do this by passing the voltage in half of each cycle and blocking the opposite-­‐polarity voltage in the other half of the cycle. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary (5) § The bridge-­‐rec:fier circuit is the preferred full-­‐wave rec:fier configura:on. § The varia:on of the output waveform of the rec:fier is reduced considerably by connec:ng a capacitor C across the output load resistance R. The resul:ng circuit is the peak rec:fier. The output waveform then consists of a dc voltage almost equal to the peak of the input sine wave, Vp, on which is superimposed a ripple component of frequency 2f (in the full-­‐wave case) and of peak-­‐to-­‐
peak amplitude Vr = Vp/2fRC. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary (6) § Combina:on of diodes, resistors, and possible reference voltage can be used to design voltage limiters that prevent one or both extremi:es of the output waveform from going beyond predetermined values – the limi:ng levels. § Applying a :me-­‐varying waveform to a circuit consis:ng of a capacitor in series with a diode and taking the output across the diode provides a clamping func:on. § By cascading a clamping circuit with a peak-­‐rec:fier circuit, a voltage doubler is realized. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Summary (6) § Beyond a certain value of reverse voltage (that depends on the diode itself), breakdown occurs and current increases rapidly with a small corresponding increase in voltage. § Diodes designed to operate in the breakdown region are called zener diodes. They are employed in the design of voltage regulators whose func:on is to provide a constant dc voltage that varies li\le with varia:ons in power supply voltage and / or load current. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033)