# Dalibor Biolek, TU and MA Brno, Czech Republic Computer supported analysis of linear systems.

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Dalibor Biolek, TU and MA Brno, Czech Republic biolek@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: R2*Rz R2*Rz Kv = ------------------------------ R1*Rz +R2*Rz +R2*R1 R1*Rz +R2*Rz +R2*R1

Typical solved problems Simple computations: Maxwell-Wien bridge - compute balance condition. Result: Rx R = R1 R2 Lx = R1 R2 C

Typical solved problems Simple computations: Voltage divider - compute voltage transfer function and derive the condition of frequency compensation. Results: Kv= Kv=(1+s*R1*C1)/[2+s*R1*(C1+C2)] R1*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.

Simple computations: Compute all two-port parameters including wave impedances. Typical solved problemsResults:

Simple computations: Transistor amplifier - verify results mentioned below. Typical solved problems

Simple computations: Colpitts oscillator - derive oscillation condition. Typical solved problems Result: h21e=C2/C1=100, then wosc=sqrt[(1+h21)/(L*C2)], fosc=wosc/(2*pi)=715 kHz.

Simple computations: Resonant circuit - find step response. Typical solved problems Result: 0.1596*exp(-50000*t)*sin( 626703*t)

Verification of the circuit principle: Noninverting amplifier with ideal OpAmp. Typical solved problems Result: Kv = 1+R1/R2 = 101

Verification of the circuit principle: Inverting amplifier with Current-Feedback Amplifier (CFA). Typical solved problems Result: Kv = -R2/R2 = -10

Verification of the circuit principle: FDNR in series with resistance. Typical solved problems Result:Zin=R1/2+1/(D*s^2)D=2*R3*C1^2

Verification of the circuit principle: Lowpass current-mode filter with current conveyor CCII-. Typical solved problems Result: 1 Ki = ------------------------------------- s^2+sC2(R1+R2)+R1R2C1C2 s^2+sC2(R1+R2)+R1R2C1C2w0^2=1/(R1R2C1C2)f0=w0/(2*pi)=10kHzQ= sqrt(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: 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: 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 

Special effects: Resonant circuit - circuit tuning (working with Dependence Editor). Typical solved problems

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 - S ymbolic N etwork A nalysis P rogram

Program conception SNAP - S ymbolic N etwork A nalysis P rogram

Program conception SNAP - S ymbolic N etwork A nalysis P rogram

SNAP - Available Circuit Elements

SNAP - Schematic Editor component bar editor modes bar input/output circuit analysis workplace for drawing

SNAP - Analyzer twoport functions column of the circuit functions line help

SNAP - Analyzer semisymbolicanalysis: symbolicanalysis: 11 1 1 CsR K V   se eK V   51 1 51 fraction line

SNAP - Analyzer no zeros pole –1e5 step response – response to the unity (Heaviside) step pulse response – response to the unity (Dirac) impulse

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