Page -16.002 Circuits and SystemsFinal ReviewJason KimPage 06.002 Circuits and Systems: Outline of Topics• Resistor Networksconcepts: Node Method, KCL, KVL, Superposition, Thevenin and Norton equivalent circuitmodels, Multiport Networks, Transformers, Power.•1st Order Circuitsconcepts: Consituitive Laws, RC netwroks, RL networks, Homogenous and Particular solution,Time constant , response to an impulse, power, Low/High/Band/Notch pass filters,sinusodial steady-state, transients, Impedance Model, Bode Plots(Magnitude and Phase).•2nd Order Circuitsconcepts: LC networks, LRC networks, damping coefficient , natural frequency ,Underdamped/Critical/Overdamped Systems, Resonance, Q factor, Half-power point,Sinusodial steady-state, transients, Power(real/reactive), Impedance Model, ELI ICE,Bode Plots(Magnitude and Phase).• Digital Abstractionconcepts: Boolean Logic(truth table, formula, gates, and transistor level), primitive laws,DeMorgan’s Law(formula and gate equivalent), MSP(minumum sum of products),MPS(minimum product of sums).• MOSFET Transistorsconcepts: Large Signal Model(S, SR, SCS, SVR), Small Signal Model, Saturation/Linear Region,Ron, Loadline, Operating Point, Input/Output Resistence, Current Gain, Power Gain,Noise Margin.• Op-Amp Circuitsconcepts: Single/Multiple input op-amp circuits, differentiator, integrator, adder, subtractor, op-amp with R,L,C, negative feedback, positive feedback, Bode Plots(Magnitude andPhase), Input/Output resistence, Schmitt Trigger, Hysteresis, Cascaded stages.• Diodesconcepts: i-v characteristics, model, diode w/ R, L, C, and op-amp, Peak detection, Clipper circuits,Incremental Analysis.τα ωoPage 11. Primitive ElementsResistor: time domain: freq. domain:Series: Parallel:• Resistor NetworkN-unknowns & N-equations (most primitive approach)Node Analysis (KCL, KVL)*KCL: Sum of all currents entering and leaving a node is zero.*KVL: Sum of all voltages around a closed loop path is zero. (be careful with polarities)1) LABEL all current directions and voltage polarities. (Remember, currents flow from + to -)2) write KCL & KVL Equation.3) substitute and solve.Simplification (by inspection)• Thevenin Equivalent Circuit Model Norton Equivalent Circuit Model* Three variables: Vth=Voc, Rth=RN, and IN=Isc . They are related by Voc=Isc*Rth .* Vth=Voc: Leave the port open(thus no current flow at the port) and solve for Voc. For a resistive network, this gives you a point on the V-axis of the i-v plot.* IN=Isc: Short the port(thus no voltage across the port) and solve for Isc flowing out of + andinto -. For a resistive network, this gives you a point on the I-axis of the i-v plot.* Rth: Set all sources to zero, except dependent sources. Solve the resistive network. When setting sources to zero, V source becomes short and I source becomes open. Rth may also be found by attaching Itest and Vtest and setting Rth = (Vtest)/(Itest). If dependent sources are present, set only the independent sources to zero and attach Itestand Vtest. Use KCL and KVL to find the expression (Vtest)/(Itest)=Rth.* For both Thevenin & Norton E.C.M.’s, they have the same power consumption at the port asthe original circuit, but not for its individual components. Power dissipated at Rth does notequal power dissipated at the resistors of the original circuit. Same holds for the powerdelivered by the sources in the Thevenin model and the original circuit. Thevenin and NortonE.C.M.’s are for terminal i-v characteristics only.• Power = Real Power = IV = I2R = V2/R (energy dissipated as heat)•VIR= ZR=R1R2+ R1R2||R1R2R1R2+-------------------=+-R1R2VoVi+-R2I2ViR1IiVoR2R1R2+--------------------Vi=I2R1R1R2+--------------------Ii=Voltage DividerCurrent Divider+-RthVthVoc=VthRNINIsc=INsame i-v characteristics at the ports+-+-NItest+-VtestOriginal Circuitnote the direction of Itestand polarity of Vtest.RthVtestItest------------=Power〈〉1T---It()Vt()td0T∫=Page 2• Superposition"In a linear network with a number of independent sources, the response can be found bysumming the response to each independent sources acting alone, with all other independentsources set to zero."1) Leave one source on and turn off all other sources.(Voltage source "off" = short & Current source "off" = open)2) Find the effect from the "on" source.3) Repeat for each sources.4) Sum the effect from each sources to obtain the total effect.For cases where a linear dependent source is present along with multiple independent sources,DO NOT turn off the dependent source. Leave the dependent source on and carry it in yourexpressions. Tackle the dependent source term last by solving linear equations. Remember thatthe variable which the dependent source is depended on is affected by the individual independentsources that you are turning on and off.• Multiport Network* By attaching V1, I1 and V2,I2 at the ports,The first subscript denote the place(port) of voltage measurement.The second subscript denote the place(port) of current source.Thus, R12 means the resistance V1/I2 when voltage V1 is measured at open port 1 and I2current source is placed at port 2.* If all the Z-parameters(Rxx’s) are identical, then the networks can’t be differentiated using onlythe i-v characteristics at the ports.* Reciprocity: R12=R21.* Using the definitions from above,Linear Networkwith n sourcesR+_VRVRVR1V2 n∼0=VR2V1V,3 n∼0=… VRnV1 n 1–∼0=++=MR22R11+-+-R21i1R12i2+-V2i2+-V1i1+-V1i1+-V2i2Mz-parameter modelV1R11I1R12I2+=V2R21I1R22I2+=R22-R21R11-R12R12=R21+-V2i2+-V1i1MT model+-Vi2+-V1i1M-G12=-G21G22+G21G11+G12 modelπVR when only V1 is on.Page 3• Transformer & . Turns Ratio =Reflected Resistance: the equiv. resistance seen at port 1, of the resistance on the other side, port2.Transformer vs. Voltage Divider : Voltage divider uses a series of resistors to divide and obtain ascaled-down voltage. In doing so, power is dissipated not only at the load but also in the seriesresistors as well, resulting in unwanted power dissipation. On the other hand, a transformerconverts its voltage through magnetic coupling and power is dissipated only in the load. Thus, nounwanted power dissipation. (assuming ideal transformers)Capacitor: time domain: freq. domain:High Frequency = Short & Low Frequency = OpenSeries: Parallel:Vc(0-)=Vc(0+) except when the input source is an impulse.Vc(t) is continuous while Ic(t) may be discontinuous."I C E" : Current(I) LEADS
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