AC_Analysis

Question 1

What is a inductor?

What is inductance?

Answer 1

An inductor is composed of a coil of wire wound around a supporting core.

The inductor voltage is determined by the magnetic field which in turn is produced by the current flowing around the coil.

The voltage is directly proportional to the inductance and the rate of change of the current.

So a constant current will produce 0 V across an inductor, like a short circuit

Question 2

Why can a current not change abruptly across a inductor?

Answer 2

Doing so would require or produce an infinitely large voltage which cannot exist in practice.

Question 3

What is a capacitor?

Answer 3

A capacitor is composed of two conductors separated by an insulator** or **dielectric material.

A voltage applied to a capacitor creates opposite electrical charges on the two conductors which in turn generate an electric field between them

Question 4

What is capacitance ?

Eq?

Answer 4

The separation (d) and area of the conductors (A), and the permittivity of the insulator/dielectric determine the capacitance in Farads (F).

Question 5

Voltage Current relationship of a capacitor?

Answer 5

The current is directly proportional to the capacitance and the rate of change of the voltage.

So a constant voltage will produce zero current into or out of the capacitor’s terminals, like an open circuit.

Question 6

Why can’t the voltage change abruptly across a capacitor?

Answer 6

It would require or produce an infinitely large current which cannot exist in practice.

dv would be a lot larger than dt, meaning that i has to be really large.

Question 7

The Phasor ?

Answer 7

Is a complex number representing a sinusoidal function

Question 8

Phasor Question

Answer 8

Question 9

Why is e^-j(pi/2) = -j ?

Answer 9

e^-j*θ = cos(θ) - j*sin(θ)

e^-j(pi/2) = cos(pi/2) - j*sin(pi/2)

e^-j(pi/2) = -j(1)

e^-j(pi/2) = -j

Question 10

Inductor Voltage-Current Relationship Eq?

Answer 10

Question 11

Capacitor Voltage-Current Relationship?

Answer 11

Question 12

What is Impedance ?

Answer 12

The impedance is simply the ratio of the voltage phasor to the current phasor of any circuit element or terminals.

Because of the presence of j and ω, the impedance of the inductor and capacitor is complex and frequency dependent.

Question 13

For a capacitor and Inductor, state what leads what.

Answer 13

From the equation V = jωLI, the inductor voltage leads its current by 90˚
From the equation V = I / jωC, the capacitor current leads its voltage by 90˚.

Question 14

What is the impedance of a resistor?

Answer 14

A resistor has an impedance which is equal to its resistance and therefore purely real.

Question 15

How do you find the current phasor of a circuit?

Answer 15

You first convert the voltage to its phasor equivalent.

Next, you find out the individual impedances of the circuit elements, add them and then use V/I = z to find the current phasor.

Question 16

How would you find voltage phasor of a capacitor and then find the stead state eq?

Answer 16

Find voltage phasor using V = I / jωC

The steady state can be found by knowing omega, and plugging the values back in

v = V_m * cos(ω*t + ϕ)

Question 17

By finding the impedance at terminals a and b, calculate the current phasor of the following circuit.

Answer 17

Question 18

What are the two parts that make up impedance and what are they called ?

Answer 18

The impedance Z is in general a complex quantity…

…where the real part is the resistance and the imaginary part is the reactance. Therefore the inductor has a positive reactance while the capacitor has a negative reactance.

Question 19

Why does a capacitor have negative reactance?

And always seem to have negative impedance?

Answer 19

Question 20

What is admittance?

Answer 20

The admittance (Y) is the reciprocal of the impedance.

The real part is the conductance and the imaginary part is the susceptance. Therefore the capacitor has a positive susceptance while the inductor has a negative susceptance.

Question 21

What are filters?

Answer 21

Filters are frequency-selective circuits that allow you to pass or attenuate different electronic signals based on their frequencies.

Filters are described by their complex transfer function H(j ω) which is the ratio of the output to input voltage phasors and is therefore a function of the signal frequency ω.

Question 22

complex transfer function vs. frequency of a low pass filter?

Answer 22

Question 23

complex transfer function vs. frequency of a High pass filter?

Answer 23

Question 24

complex transfer function vs. frequency of a bandpass filter?

Answer 24

Question 25

complex transfer function vs. frequency of a bandstop filter?

Answer 25

Question 26

Simple RC Circuit Inspection

Answer 26

At DC or very low frequencies, the capacitor impedance is much larger than the resistance. Thus the magnitude of the output voltage ≈ input voltage.

At very high frequencies, the capacitor impedance becomes very small, like a short circuit, compared to the resistance. So the output voltage magnitude will be very small also.

Since this circuit passes the input signal voltage to the output at low frequencies but attenuates the output voltage at high frequencies, it is therefore a low-pass filter.

Question 27

What is a passband and what is a stopband?

Answer 27

A passband is when the complex tranfer function is almost equal to 1. Or in other words when Vo is equal to Vi.

A stopband is when the complex transfer function is lmost equal to 0. This happens wen Vo is alot smaller than Vi.

Question 28

Why is this not an real depiction of a complex transfer function ?

Answer 28

Real filters do not have abrupt band transitions

Question 29

Written in this form, how are the stopband and passband defined ?

Answer 29

stopband: when (ωRC)² >>1 H(j ω) ≈ 0
passband: when (ωRC)² << 1 H(j ω) ≈ 1

Question 30

!

How is the cuttoff frequency defined?

Answer 30

The cutoff frequency is defined as the frequency at which the transfer function magnitude is equal to 1/√(2) from its maximum value.

Question 31

For a low pass filter how can the cutt off frequency be found?

Answer 31

Question 32

How does the phase difference between the output and input voltages change for values of (ωRC)² ?

Answer 32

When (ωRC)² >> 1 ∠H(j ω) ≈ 0º

When (ωRC)² << 1 ∠H(j ω) ≈ -90º

Question 33

What is the phase difference of the output and input voltages at the cutoff frequency ?

Answer 33

Question 34

How do you get from 1/(1+j) to 45 degrees ?

Answer 34

Simplify the complex number further by taking the conjugate and then splitting the fraction.

Now the complex number should be in the form a + jb, and the angle can be calculated.

Question 35

Howis the ∠H(j ω) ≈ -90 when (ωRC)² << 1 ?

Answer 35

Question 36

How do you get to 1/√(LC)?

Answer 36

Equate ωL and 1/ωC

Question 37

What do the w’s mean, what does the b mean ?

Answer 37

The upper cutoff frequency: ω_c2

The lower cutoff frequency: ω_c1

The bandwidth: B

Question 38

What is the Q factor?

Answer 38

Question 39

If you’re have the complex transfer function and you have Vi, how do you calculate Vo ?

Answer 39

Through…