dalibor biolek, tu and ma brno, czech republic [email protected] computer supported analysis of...

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


Simple computations:Maxwell-Wien bridge - compute balance condition.

Result: Result:

Rx R = R1 R2Rx R = R1 R2

Lx = R1 R2 CLx = R1 R2 C


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


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.


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.


Simple computations:Colpitts oscillator - derive oscillation condition.


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.


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.


Result:Result:

Kv = 1+R1/R2 = 101Kv = 1+R1/R2 = 101

Verification of the circuit principle:Inverting amplifier with Current-Feedback Amplifier (CFA).


Result:Result:

Kv = -R2/R2 = -10Kv = -R2/R2 = -10

Verification of the circuit principle:FDNR in series with resistance.


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-.


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...


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.


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.


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).


-3

0

frequency

mag. in dB

B

f0

Special effects:Resonant circuit - circuit tuning.


• 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


EDIT .snn

.cir

PSched .net

.sch

netlist

.m, .mpl,

.mcd, .txt

outputs for

SNAP

SNAP.LIB

SNAP.CDL

following processing

Program conception


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 - 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

dalibor biolek, tu and ma brno, czech republic [email protected] computer supported analysis of...

Documents

typical problems

r1 slide

typical solved problems

typical solved problemsresults

c2 slide

r1 r2 c slide

rz r2

r1 r2 lx