ELE 404 Module 1 Resistors act as a conductor and they are linear The initial condition is represented by an impulse current source in time domain. The initial condition is represented by a constant current source in Laplace domain. How to remove the input : (i) For a voltage input, replace it with a short-circuit. (ii) For current input, replace it with an open-circuit. How to get output impedance : Obtained by applying a test voltage source vx (or a test current source ix ) at the output terminals, removing the input of the network, and measuring the resultant current ix (or voltage vx ) : Two conditions to represent as Norton equivalent circuit: Thevenin Equivalent Circuit An electric network can be represented by a Thevenin voltage source VT in series with a Thevenin impedance ZT Both the network and its Thevenin equivalent must have the same terminal behaviour Small signal equivalent circuit An electrical signal often consists of a large time-invariant component VDC (DC component) and a small time-varying component v (AC component). The DC component is typically used to set an appropriate operating point of electronic devices while the AC component carries the information to be processed by electronic devices. The circuit that depicts the behavior of the AC component of currents/voltages... of an electric network is termed the small-signal equivalent circuit or AC circuit of the network. Why do we need small signal equivalent circuit? Some electronic devices diodes, transistors are not linear. The resistor which is linear and easy to study the behaviour of it whereas its hard to study the behaviour of the nonlinear devices because they have a small amplitude. Thus, electronic device can be linearized at fix DC operating point through small signal equivalent circuits which are linear. They re linearized through Taylor series. The small-signal equivalent circuit of an independent voltage source is a short-circuit. V=0 The small-signal equivalent circuit of an independent current source is an open-circuit. I=0 Transfer function : The ratio of the output to the input in AC steady-state at which t → infinity Frequency response : The transfer function of a network in AC steady-state. Initial conditions have no impact on frequency response. Poles : Obtained by setting the denominator to zero Zeros : Obtained by setting the numerator to zero Bode plots are the (i) magnitude plot and (ii) phase plot of the transfer function of a network in AC steady-state. No overshoot in magnitude plot because sp1 is the dominant pole as it sets the bandwidth, i.e the frequency at which |A(jw)| drops by 3 dBapproximately. What is the value of the overshoot of the Bode plot (magnitude) of a second-order network with a pair of complex conjugate poles ? At wo with Q (Quality Factor)=1/2 Complex conjugate poles are often preferred to eliminate loss at wo → In order to have no loss at wo, Q = 1 is required. Q (quality factor) : Quantifies the amount of overshoot. What is the loss of the Bode plot (magnitude) of a first-order system at its -3 dB frequency wb is the bandwidth or w-3B at which magnitude attenuation is 3 dB? What is the loss of the Bode plot (magnitude) of a second-order system at its -3 dB frequency? Floating element Z can be replaced with single-ended elements Z1 and Z2 if the two networks have (i) the same branch current and (i) the same nodal voltages Why the initial condition of the capacitors of a network plays no role in the steady-state behavior of the network ? Because at that time the capacitors are not fully charged. What is the loss of the Bode plot (magnitude) of a first-order system at its -3 dB frequency? What is the loss of the Bode plot (magnitude) of a second-order system at its -3 dB frequency? For second-order systems, complex conjugate poles are often preferred to minimize the loss of magnitude at wo. The amount of overshoot at wo is set by quality factor. The initial condition of a capacitor can be represented by an impulse current source Cv(0-)(delta t) or a constant current source Cv(0-) in time and frequency domains, respectively. The direction of the current is the opposite of the voltage gradient.
