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Computer supported analysis of linear systems

Explore practical demonstrations and solved problems in linear systems analysis with SNAP, a powerful tool for circuit analysis. Learn about limitations, special effects, and circuit principles verification. Enhance your understanding of circuitry with symbolic and numerical analysis.

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Computer supported analysis of linear systems

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  1. Computer supported analysis of linear systems Dalibor Biolek, TU and MA Brno, Czech Republic biolek@cs.vabo.cz

  2. Lecture Outline • Typical problems which are often solved • Limitations of professional simulators • SNAP conception and features • Practical demonstration

  3. Typical solved problems Simple computations: Loaded voltage divider - compute voltage transfer function. Result: R2*Rz Kv = ------------------------------ R1*Rz +R2*Rz +R2*R1

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

  5. Typical solved problems Simple computations: Voltage divider - compute voltage transfer function and derive the condition of frequency compensation. Results: Kv= (1+s*R1*C1)/[2+s*R1*(C1+C2)] R1*C1 = R2*C2

  6. 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.

  7. Results: Typical solved problems Simple computations: Compute all two-port parameters including wave impedances.

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

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

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

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

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

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

  14. Typical solved problems Verification of the circuit principle: Lowpass current-mode filter with current conveyor CCII-. Result: 1 Ki = ------------------------------------- s^2+sC2(R1+R2)+R1R2C1C2 w0^2=1/(R1R2C1C2) f0=w0/(2*pi)=10kHz Q= sqrt(C1/C2*R1*R2)/(R1+R2) = 5

  15. Typical solved problems Verification of the circuit principle: DC precise LP filter. Frequency response looks good, but... Result: filter poles: -971695 + j484850 -971695 - j484850 -321953 195172 + j461620 195172 - j461620 FILTER IS UNSTABLE!

  16. Results: Kv = 2*pi*GBW/[s+2*pi*GBW*(1+1/A0)] = 62831853/(s+ 6283217) Typical solved problems Influence of real properties: Operational amplifier as voltage follower - single-pole model.

  17. Typical solved problems Influence of real properties: Sallen-Key LP filter- influence of OpAmp properties. OpAmp one-pole model: A0=200k, GBW=1MEG, R0=75 

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

  19. Typical solved problems Special effects: Resonant circuit - circuit tuning.

  20. Limitations of typical professional simulators • 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

  21. „S.E.E.R. - Family Programs“ 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

  22. SNAP - Symbolic Network Analysis Program • 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..

  23. SNAP - Symbolic Network Analysis Program Program conception

  24. SNAP - Symbolic Network Analysis Program Program conception

  25. SNAP - Symbolic Network Analysis Program

  26. SNAP - Available Circuit Elements

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

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

  29. symbolic analysis: 1 = K V + 1 sR C 1 1 1 = K 1 e 5 V + 1 e 5 s SNAP - Analyzer fraction line semisymbolic analysis:

  30. 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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