Time 0s 1m s 2m s 3m s 4m s 5m s 6m s 7m s 8m s 9m s 10m s V(out) AVG (V(out)) 0V 20V 40V V(error) AVG (V(error)) -20V 0V 20V V(control) AVG (V(control)) 0V 10V 20V SEL>> AVG (V(out)) V(out) V(error) AVG (V(error)) V(control) AVG (V(control)) Chapter 9 Simulation of Switching Converters
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Chapter 9 Simulation of Switching Converters. Power switching convertersSimulation of switching converters2 Overview PSpice PSpice Simulations using.CIR.
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Power switching converters Simulation of switching converters 43
PSpice simulations using vendor models
TL084
+
-
V+
V-
D1
MUR420
sense
L1
10mHIC = 0
R7
1
0
0
pwm_out
-15
saw
R6
100
+15
Vref
out
+15
R3
100k
R5
3k
R4
1k
V4TD = 0
TF = 1nPW = 1nPER = 1m
V1 = 0
TR = 999u
V2 = 10
pwm
R2
300k
R8
300
PWM modulator
5
control
V110Vdc
Error amplifier
C1
100uF
LM311
+
-GV
+V
-
B/S B
R1
20
0
X2
MTP15N05E/MC ESR10m
-15
+
-
.TRAN 0 30m 0 0.1u
.OPTIONS STEPGMIN
.OPTIONS ABSTOL= 10p
.OPTIONS ITL1= 400
.OPTIONS ITL4= 500
.OPTIONS RELTOL= 0.01
.OPTIONS VNTOL= 10u
Power switching converters Simulation of switching converters 44
PSpice simulations using vendor models
Time
0s 5ms 10ms 15ms 20ms 25ms 30msV(out)
0V
10V
20V
SEL>>
V(control)4.8V
5.0V
5.2VI(L1)
0A
2.0A
4.0A
Power switching converters Simulation of switching converters 45
Vorperian models for PSpice
Power switching converters Simulation of switching converters 46
Vorperian models for PSpice
Power switching converters Simulation of switching converters 47
Vorperian models for PSpice
Power switching converters Simulation of switching converters 48
Vorperian models for PSpice **** VMSSCCM ***** Small signal continuous conduction voltage mode model* Params: RMPHITE --> External ramp height * D --> Duty cycle* Ic --> Current flowing from terminal C* Vap --> Voltage across terminal A P* Rsw --> Switch on resistance* Rd --> diode on resistance* Rm --> which models the base storage effects* Re --> models ripple across esr of cap* Pins control voltage -- * common -------- |* passive----- | |* active -- | | |.subckt VMSSCCM A P C VC Params: RMPHITE=2 D=0.4 IC=1 VAP=20 + Rsw=1e-6 Rd=1e-6 Re=1e-6 Rm=1e-6 efm 4 0 value =v(Vc)/rmphite e2 A 6 value=v(0,4)*Vap/d g1 A P value=v(4)*IC gxfr 6 P VALUE=I(vms)*D exfr 9 P VALUE=V(6,P)*D vms 9 8 0 rd 8 C d*rd+(1-d)*rsw+d*(1-d)*re+rm rope 4 0 1g rgnd 0 P 1g.ends
Power switching converters Simulation of switching converters 49
Small-signal analysis of switching converters
R20
0
U7
VMSSCCM
D = 0.5IC = -1.84
RD = 1e-6
RE = 10mRM = 1e-6
RMPHITE = 10
RSW = 10mVAP = -17.6
1
3
2
4
A
C
P
VC
Rs1300k
out
Rs
1
Resr10m
V110Vdc0
L1
10mHIC = 0
Rs2
100k
sense
V41Vac0Vdc
Cout
100uFIC = 0
+
-
Small-signal AC analysis
Power switching converters Simulation of switching converters 50
Small-signal analysis of switching converters
Time
0s 5ms 10ms 15ms 20ms 25ms 30msV(OUT)
0V
10V
20V
SEL>>
I(L1)0A
1.0A
2.0A
3.0A
Power switching converters Simulation of switching converters 51
Power switching converters Simulation of switching converters 73
Creating capture symbols for PSpice simulation
•Vendors often provide PSpice models for their circuit components. They are normally provided in a text file with extension .LIB; if the file has a different extension, it should be changed to .LIB •Start the PSpice Model Editor and from the File menu, choose Create Parts •Browse to find the input model library (.LIB file) and click OK to start •This step creates an .OBL file with a schematic symbol linked to your model •To place the new part into the schematic, open Capture, and from the Place menu choose Part. Click Add library, then find and add the new “.OLB” file
Power switching converters Simulation of switching converters 74
Solving convergence problems PSpice uses the Newton-Raphson algorithm to
solve the nonlinear equations in these analyses
The algorithm is guaranteed to converge only if the analysis is started close to the solution
If the initial guess is far away from the solution, this may cause a convergence failure or even a false convergence
If the node voltages do not settle down within a certain number of iterations, an error message will be issued
Power switching converters Simulation of switching converters 75
DC analysis error messages The DC Analysis calculates the small-signal bias
points before starting the AC analysis or the initial transient solution for the transient analysis
Solutions to the DC analysis may fail to converge because of incorrect initial voltage guesses, model discontinuities, unstable or bistable operation, or unrealistic circuit impedances
When an error is found during the DC analysis, SPICE will then terminate the run because both the AC and transient analyses require an initial stable operating point in order to start
Power switching converters Simulation of switching converters 76
DC analysis error messages
No convergence in DC analysis
PIVTOL Error
Singular Matrix
Gmin/Source Stepping Failed
No Convergence in DC analysis at Step = xxx
Power switching converters Simulation of switching converters 77
Transient analysis error messages
If the node voltages do not settle down, the time step is reduced and SPICE tries again to determine the node voltages
If the time step is reduced beyond a certain fraction of the total analysis time, the transient analysis will issue an error message “Time step too small” and the analysis will be halted
Transient analysis failures are usually due to model discontinuities or unrealistic circuit, source, or parasitic modeling
Power switching converters Simulation of switching converters 78
Solutions to convergence problems There are two ways to solve convergence problems
the first only tries to fix the symptoms by adjusting the simulator options
while the other attacks the root cause of the convergence problems
Once the circuit is properly modeled, many of the modifications of the "options" parameters will no longer be required
It should be noted that solutions involving simulation options may simply mask the underlying circuit instabilities
Power switching converters Simulation of switching converters 79
Bias point (DC) convergence
Checking circuit topology and connectivity
Modeling of circuit components
PSpice options are checked to ensure that they are properly defined
Power switching converters Simulation of switching converters 80
Checking circuit topology and connectivity Make sure that all of the circuit connections are valid
Check for incorrect node numbering or dangling
nodes
Verify component polarity
Check for syntax mistakes
Make sure that the correct PSpice units (i.e. MEG for 1E6, not M, which means mili in simulations) are used
Power switching converters Simulation of switching converters 81
Make sure that there is a DC path from every node to ground
Make sure that there are at least two connections at every node
Make sure that capacitors and/or current sources are not connected in series
Make sure that no (groups of) nodes are isolated from ground by current sources and/or capacitors
Make sure that there are no loops of inductors and/or voltage sources only
Power switching converters Simulation of switching converters 82
Place the ground (node 0) somewhere in the circuit
Be careful when floating grounds (e.g., chassis ground) are used; a large resistor should be connected from the floating node to ground. All nodes will be reported as floating if "0 ground" is not used
Make sure that voltage/current generators use realistic values, and verify that the syntax is correct
Make sure that dependent source gains are correct, and that E/G element expressions are reasonable
Power switching converters Simulation of switching converters 83
Verify that division by zero or LOG(0) cannot occur
Voltages and currents in PSpice are limited to the range +/- 1e10
Avoid using digital components, unless really necessary
Initialize the digital nodes with valid digital values
Avoid situations where an ideal current source delivers current into a reverse-biased p-n junction without a shunt resistance
Power switching converters Simulation of switching converters 84
Setting up the options for the analog simulation
Increase ITL1 to 400 Use NODESETs to set node voltages to the nearest
reasonable guess at their DC values Enable the GMIN stepping algorithm Set PREORDER in Simulation Profiles options Setting the value of ABSTOL to 1 µ PSpice does not always converge when relaxed
tolerances are used Setting GMIN to a value between 1n and 10n will often
solve convergence problems Setting GMIN to a value, which is greater than 10n, may
cause convergence problems
Power switching converters Simulation of switching converters 85
Transient convergence
The transient analysis can fail to complete if the time step becomes too small
This can be due to either (a) the Newton-Raphson iterations would not
converge even for the smallest time step size (b) something in the circuit is moving faster than
can be accommodated by the minimum step size
Power switching converters Simulation of switching converters 86
Transient convergence
The circuit topology and connectivity should first be checked
Followed by the PSpice options
Power switching converters Simulation of switching converters 87
Circuit topology and connectivity
Avoid using digital components, unless really necessary
Initialize the nodes with valid digital value to ensure there are no ambiguous states
Use RC snubbers around diodes
Add Capacitance for all semiconductor junctions
Power switching converters Simulation of switching converters 88
Circuit topology and connectivity Add realistic circuit and element parasitics
It is important that switching times be nonzero
It is recommended that all inductors have a parallel resistor
Look for waveforms that transition vertically (up or down) at the point during which the analysis halts
Power switching converters Simulation of switching converters 89
Circuit topology and connectivity
Increase the rise/fall times of the PULSE sources
Ensure that there is no unreasonably large capacitor or inductor
Power switching converters Simulation of switching converters 90
PSpice options
Set RELTOL=.01
Reduce the accuracy of ABSTOL/VNTOL if current/voltage levels allow it
ABSTOL and VNTOL should be set to about 8 orders of magnitude below the level of the maximum voltage and current
Increase ITL4, but no more than 100
Power switching converters Simulation of switching converters 91
PSpice options
Skipping the bias point is not recommended
Any applicable .IC and IC= initial conditions statements should be added to assist in the initial stages of the transient analysis
Power switching converters Simulation of switching converters 92
Switching converter simulation using Matlab
Working with transfer functions
Consider a buck converter designed to operate in the continuous conduction mode having the following parameters: R = 4Ω, L = 1.330 mH, C = 94 µf, Vs = 42 V, Va = 12 V
1 2
2
20 0
1 1( )
( ) 1
o z zd
s ss sv s
Ks sd sQ
2(1 )
sd
VK
D
1
1z
ESR
sR C
2
2
(1 )( || ) ind
z ESR
RDs R R R
L L
0
(1 )1 ind e
ESR
R r D D
R RLC
||e ESRr R R
0
(1 ) 1( )
ind e
ESR
QR r D
L C R R
Power switching converters Simulation of switching converters 93
Power switching converters Simulation of switching converters 94
Switching converter simulation using Matlab
% polynomials are entered in descending order of S.n1=[1/Sz1 1]n2=[-1/Sz2 1]NUM=conv(n1,n2)% the convolution realizes the product of 2 polynomials% define denumeratorDEN = [1/(Wo^2) 1/(Wo*Q) 1]% create TF variablesysTF = Kd * tf(NUM,DEN)which returnsTransfer function:
-5.317e-008 s^2 - 0.05648 s + 82.32
4.913e-006 s^2 + 0.01343 s + 1sysTF
Power switching converters Simulation of switching converters 95
Switching converter simulation using Matlab
The location of the poles can be found usingpoles = roots(DEN)and the frequency response can be plotted usingbode(sysTF)
Bode Diagram
Frequency (rad/sec)
Phase
(deg)
Magn
itude
(dB
)
-40
-20
0
20
40
101
102
103
104
105
106
107
-270
-225
-180
-135
-90
-45
0
Power switching converters Simulation of switching converters 96
Switching converter simulation using Matlab
The small signal transient step response can be plotted usingFigure % this command opens a new figure windowstep(sysTF) Step Response
Time (sec)
Am
plit
ud
e
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-10
0
10
20
30
40
50
60
70
80
90
Power switching converters Simulation of switching converters 97
Switching converter simulation using Matlab
Working with matrices
Consider a buck converter designed to operate in the continuous conduction mode having the following parameters: R = 4Ω, L = 1.330 mH, C = 94 µf, Vs = 42 V, Va = 12 V.
% state-space averaged model of a Buck converterRload= 4;% load resistanceL= 1.330e-3; % inductancecap=94.e-6; % capacitanceTs=1.e-4; % switching periodVs=42; % input DC voltageVref=12; % desired output voltageThe average duty cycle is:D=Vref/(Vs); % ideal duty cycle
Power switching converters Simulation of switching converters 98