Concept Questions Chapter 5 ECE 1240

How are the ramp and rectangle functions related to the step function?

-The ramp function is given by the integral of the step function. -The rectangle function is the sum of a positive step that start at the beginning of the rectangle and a negative step that starts at the end of the rectangle.

What is the difference between the transient and steady-state components of the circuit response?

-The transient response represents the initial reaction immediately after a sudden change, such as closing or opening a switch to connect a source to the circuit. This is also called the early time response. -The steady-state response is the response that continues after the transient response goes to zero.

What causes clipping of the waveform at the output of an op-amp integrator circuit? Can clipping occur at the output of a differentiator circuit?

Clipping occurs whenever the output starts to exceed the supply voltage Vcc, which can occur in both the integrator circuit and the differentiator circuit.

An inductor stores energy through the magnetic field B, but the equation for the energy stored in an inductor is w = 1/2 Li2. Explain

The energy stored in the inductor's magnetic field is generated by the current.

For the capacitor, can p(t) be negative? Can w(t) be negative? Explain.

If p(t) is positive, it means the capacitor is charging up, and if it is negative, it means the capacitor is discharging, so p(t) can be both positive and negative. Energy w(t) is the energy stored in the capacitor, so it cannot be negative.

The voltage across a capacitor cannot change instantaneously. Can the current change instantaneously, and why?

If voltage changes in zero time (instantaneously), the current becomes infinite, which it cannot. Hence voltage cannot change instantaneously. But the converse is not true: that is, the current can change instantaneously without violating any laws.

Suppose the switch in the circuit of Fig. 5-36(a) had been open for a long time, and then it was closed suddenly. Will Is initially flow through R or L?

It will flow through R because the current through an inductor cannot change instantaneously.

What specific characteristic defines a first-order circuit?

Mathematically, the circuit is described by a first-order differential equation, and physically the circuit contains a single nonlinear element (capacitor or inductor), or multiple capacitors that can be reduced to a single capacitor, or multiple inductors that can be reduced to a single inductor.

For the natural response of an RC circuit, how does the decay rate for voltage compare with that for power?

Power decays twice as fast as voltage.

If Vs2 < Vs1 in the circuit of Fig. 5-30, what would you expect the direction of the current to be after the switch is moved from position 1 to 2? Analyze the process in terms of charge accumulation on the capacitor.

Since the new voltage is lower, the capacitor will need to loose charge. Hence, iC in Fig. 5-30(c) should be counterclockwise.

Can the voltage across an inductor change instantaneously?

The current through an inductor cannot change instantaneously, but the voltage can.

What are the three quantities needed to establish υC(t) across a capacitor in an RC circuit?

The initial voltage υC (0), the final voltage υC (infinity), and the time constant τ = RC.

What determines the maximum switching frequency for a CMOS inverter?

The maximum switching frequency of the models presented in this chapter is determined from the R-C time constant of the equivalent circuit during charging or discharging (i.e. we model a switching transistor as a resistor and a capacitor, which exhibits a decaying exponential time transient when charging or discharging that has a time constant, τ = 1/RC).

What determines the slope of a ramp waveform?

The multiplying coefficient. For υ(t) = Ar(t − 1), the slope is A.

How do the rules for adding inductors in series and in parallel compare with those for resistors and capacitors?

The rules for adding inductors in series and in parallel are the same as for resistors, but not the same as capacitors.

What does the time constant of an RC circuit represent? Would a larger capacitor discharge faster or more slowly than a small one?

The time constant defines how fast or slow the circuit responds to change. A larger capacitor means a longer time constant, and hence a slower response.

What is the rationale for adding parasitic capacitances to nodes G, D, and S in Fig. 5-48?

These capacitances model charge storage phenomena that result from both transistor physics and metal interconnects running near the transistors. They allows us to model time transients of voltages and currents as well as energy and power constraints.

If υs(t) is the input signal to a two-stage op-amp circuit with the first stage being an integrator with R1C1 = 0.01 and the second stage being a differentiator with R2C2 = 0.01, under what circumstances will the output waveform υout(t) be the same or different from υs(t)?

They will be the same if there is no clipping in either operation.

Why do we study the circuit response to dc and ac sources separately?

ac signals are periodic, so we use different math tools to analyze them than we do with dc signals.

A unit step function u(t) is equivalent to closing an SPST switch at t = 0. What is u(−t) equivalent to?

u(−t) is equivalent to opening the switch at t = 0.

Explain why a capacitor behaves like an open circuit under dc conditions.

under dc conditions dv/dt = 0. Hence i = 0, which is equivalent to an open circuit that allows no current to flow through it.

What is the approximate shape of the waveform described by the function (1 − e−|t| )?

v

Compare Eq. (5.96) with Eq. (5.107) to draw an analogy between RC and RL circuits. υC, R, and C of the RC circuit correspond to which parameters of the RL circuit?

υC in RC circuit becomes iL in RL circuit • R in RC circuit becomes 1/R in RL circuit • C in RC circuit becomes 1/L in RL circuit

If the time constant of a negative exponential function is doubled in value, will the corresponding waveform decay faster or slower?

An exponential function with a short time constant rises or decays faster than an exponential function with a longer time constant.

What type of material exhibits a magnetic permeability higher than μ0?

Ferromagnetic materials.

Compare the voltage-division equation for two capacitors in series with that for two resistors in series. Are they identical or different in form?

For resistors, υ1 is proportional to R1, whereas for capacitors, υ1 is proportional to C2.