dalibor biolek, tu and ma brno, czech republic [email protected] computer supported analysis of...
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Dalibor Biolek, TU and MA Brno, Czech Dalibor Biolek, TU and MA Brno, Czech RepublicRepublic
[email protected]@cs.vabo.cz
Computer supported analysis of linear systems
Lecture Outline
• Typical problems which are often solved
• Limitations of professional simulators
• SNAP conception and features
• Practical demonstration
Typical solved problems
Simple computations:Loaded voltage divider - compute voltage transfer function.
Result: Result:
R2*RzR2*RzKv = ------------------------------Kv = ------------------------------ R1*Rz +R2*Rz +R2*R1R1*Rz +R2*Rz +R2*R1
Typical solved problems
Simple computations:Maxwell-Wien bridge - compute balance condition.
Result: Result:
Rx R = R1 R2Rx R = R1 R2
Lx = R1 R2 CLx = R1 R2 C
Typical solved problems
Simple computations:Voltage divider - compute voltage transfer function and derive the condition of frequency compensation.
Results:Results:
Kv=Kv=
(1+s*R1*C1)/[2+s*R1*(C1+C2)](1+s*R1*C1)/[2+s*R1*(C1+C2)]
R1*C1 = R2*C2R1*C1 = R2*C2
Typical solved problems
Simple computations:Campbell filter - compute current through R2 if input voltage/frequency is 10V/5kHz.
Result: 61.4 mA/-90.6 degrees.Result: 61.4 mA/-90.6 degrees.
Simple computations:Compute all two-port parameters including wave impedances.
Typical solved problems
Results:Results:
2/1
1.0/1
12/
1.11
3222
321
3212112
3111
RRa
sRa
RRRRRa
RRa
Simple computations:Transistor amplifier - verify results mentioned below.
Typical solved problems
Simple computations:Colpitts oscillator - derive oscillation condition.
Typical solved problems
Result:Result:
h21e=C2/C1=100, then h21e=C2/C1=100, then wosc=sqrt[(1+h21)/(L*C2)],wosc=sqrt[(1+h21)/(L*C2)],fosc=wosc/(2*pi)=715 kHz.fosc=wosc/(2*pi)=715 kHz.
Simple computations:Resonant circuit - find step response.
Typical solved problems
Result:Result:
0.1596*exp(-50000*t)*sin( 626703*t)0.1596*exp(-50000*t)*sin( 626703*t)
Verification of the circuit principle:Noninverting amplifier with ideal OpAmp.
Typical solved problems
Result:Result:
Kv = 1+R1/R2 = 101Kv = 1+R1/R2 = 101
Verification of the circuit principle:Inverting amplifier with Current-Feedback Amplifier (CFA).
Typical solved problems
Result:Result:
Kv = -R2/R2 = -10Kv = -R2/R2 = -10
Verification of the circuit principle:FDNR in series with resistance.
Typical solved problems
Result:Result:
Zin=R1/2+1/(D*s^2)Zin=R1/2+1/(D*s^2)D=2*R3*C1^2D=2*R3*C1^2
Verification of the circuit principle:Lowpass current-mode filter with current conveyor CCII-.
Typical solved problems
Result:Result:
11Ki = -------------------------------------Ki = ------------------------------------- s^2+sC2(R1+R2)+R1R2C1C2s^2+sC2(R1+R2)+R1R2C1C2
w0^2=1/(R1R2C1C2)w0^2=1/(R1R2C1C2)f0=w0/(2*pi)=10kHzf0=w0/(2*pi)=10kHzQ=Q=sqrt(C1/C2*R1*R2)/(R1+R2) = 5sqrt(C1/C2*R1*R2)/(R1+R2) = 5
Verification of the circuit principle:DC precise LP filter. Frequency response looks good, but...
Typical solved problems
Result:Result:filter poles:-971695 + j484850-971695 - j484850-321953 195172 + j461620 195172 - j461620
FILTER IS UNSTABLE!
Influence of real properties:Operational amplifier as voltage follower - single-pole model.
Typical solved problems
Results:Results:
GBW
-20dB/decade=
-6 dB/octave
0
frequency
mag. in dB
A in dB
follower
OPA
f0
A-3dB
Kv = 2*pi*GBW/[s+2*pi*GBW*(1+1/A0)] = 62831853/(s+ 6283217)Kv = 2*pi*GBW/[s+2*pi*GBW*(1+1/A0)] = 62831853/(s+ 6283217)
Influence of real properties:Sallen-Key LP filter- influence of OpAmp properties.
Typical solved problems
OpAmp one-pole model:A0=200k, GBW=1MEG, R0=75
100 500 1k 5k 10k 50k100k 500k 1M 5M
-100
-80
-60
-40
-20
0
20
frequency
mag. in dB
ideal
real
Special effects:Resonant circuit - circuit tuning (working with Dependence Editor).
Typical solved problems
-3
0
frequency
mag. in dB
B
f0
Special effects:Resonant circuit - circuit tuning.
Typical solved problems
• Only numerical analysis, not symbolic and semisymbolic
• Zeros and poles are not available
• Too complicated models, impossible to study influence of partial component parameters
• Sensitivity analysis is not available
Limitations of typical professional simulators
S.E.E.R. - Société d'Etudes d'Exploitation et de Recherches
49, rue Saint-Didier
75116 PARIS
FRANCE
NAFID - Computer Supported Design Of Analog Filters
SNAP - Universal Linear Circuit Analyzer
http://www.seer.fr
„S.E.E.R. - Family Programs“
• Symbolic and semisymbolic analysis
• Zeros and poles, waveforms equations
• Numerical analysis in the frequency and time domains
• Sensitivity analysis
• Special effects (Dependence Editor..)
• Behavioral models based on MNA
• Export to MATLAB, MATHCAD, MAPLE..
SNAP - Symbolic Network Analysis Program
Program conception
SNAP - Symbolic Network Analysis Program
EDIT .snn
.cir
PSched .net
.sch
netlist
.m, .mpl,
.mcd, .txt
outputs for
SNAP
SNAP.LIB
SNAP.CDL
following processing
Program conception
SNAP - Symbolic Network Analysis Program
schematic editor
netlist
compilation of symbolic equations
circuit function in the symbolic form deflation ofcircuit matrix
eigenvalue problem
editorlibrary
modellibrary
compilation of numeric equations
circuit function in the semisymbolic form
SNAP - Symbolic Network Analysis Program
SNAP - Available Circuit Elements
SNAP - Schematic Editor
component bar
editor modes bar
input/output circuit analysis
workplacefor drawing
SNAP - Analyzer
twoport functions
column of thecircuit
functions
line help
SNAP - Analyzer
semisymbolic analysis:
symbolic analysis:
111
1
CsRKV
seeKV
51
151
fraction line
SNAP - Analyzer
no zeros
pole –1e5
step response – response to the unity (Heaviside) step
pulse response – response to the unity (Dirac) impulse
teth 1000001
teetg 10000051