Chapter 4: Ac circuits and Passive filters

Question 1

What is bandwidth?

Answer 1

The range of frequencies required to make up a signal

Question 2

What is the bandwidth if the signal is a sine wave?

Answer 2

zero

Question 3

What is the bandwidth if the signal is a square wave?

Answer 3

infinite-infinite series of sine waves

Question 4

What is a passive filter?

Answer 4

They are made from combinations of resistors, capacitors and inductors. They can suppress certain frequencies within a frequency spectrum.

Question 5

What does a low pass filter do?

Answer 5

Low pass filter allows low frequency signals to pass through unaffected but blocks high frequency signals

Question 6

What does a high pass filter do?

Answer 6

Allows high frequency signals to pass through unaffected but blocks low frequency signals

Question 7

What does a band filter do?

Answer 7

Only allows a certain ‘band’ of frequencies to pass through unaffected. Any signal higher or lower than the band is blocked

Question 8

In AC circuits, capacitors don’t have resistance but ________.

Answer 8

Reactance

Question 9

Give the symbol for capacitive reactance

Answer 9

Xc

Question 10

Give the equation for capacitive reactance

Answer 10

Xc=1/2πfC

Question 11

What is reactance measured in?

Answer 11

Ohms

Question 12

What does the graph of reactance against frequency look like

Answer 12

negative curve due to the 1/

Question 13

What is impedance?

Answer 13

The combined effect of resistance and reactance

Question 14

Give the equation for impedance

Answer 14

Z=√R²+Xc²
Z=impedance
Units=Ohms

Question 15

Draw a low pass filter circuit

Answer 15

Look at notes for diagram. Positive and negative rails in parallel.
R on the positive. Connection from positive to negative. Capacitor on the connection.

Question 16

State the voltage divider equation in terms of a low pass filter

Answer 16

Vout=Vin/Z x Xc

Question 17

How to calculate the voltage gain for a low pass filter?

Answer 17

Xc/Z or Vout/Vin

Question 18

At a low frequency what does the voltage divider for a low pass filter change to

Answer 18

xc²»R²
R² is negligible compared to Xc² so it is ignored
Xc/√Xc² =1

Question 19

At a high frequency what does the voltage divider for a low pass filter change to

Answer 19

R²»Xc²
Xc² is negligible compared to R²
Vout=Xc/2πfC

Question 20

What is the break frequency?

Answer 20

When Xc=R

Question 21

How to calculate Vout at the break frequency

Answer 21

Vout≈0.7 x Vin

Question 22

On log paper, where is the break frequency

Answer 22

At 45 degrees

Question 23

Draw a High pass filter circuit

Answer 23

Look at notes for diagram. Positive and negative rails in parallel.
C on the positive. Connection from positive to negative. Resistor on the connection.

Question 24

Give the potential divider equation in terms of a high pass filter circuit

Answer 24

V0=Vin/Z x R

Question 25

How to calculate the voltage gain for a high pass filter?

Answer 25

Vgain=R/Z

Question 26

At a high frequency what does the voltage divider for a high pass filter change to

Answer 26

R²»Xc²
So Vout=Vin/R

Question 27

At a low frequency what does the voltage divider equation for a high pass filter change to

Answer 27

Xc²»R²
R² is negligble
So Vout=Vin/Xc x R

Question 28

How to calculate voltage gain of a high pass filter at low frequency

Answer 28

2πfC

Question 29

What problem arises when connecting a filter output to the next stage in a system?

Answer 29

For a high pass filter, the input resistance of the next stage will be in parallel with the R, changing the effective resistance.
Due to R and C determining the frequency response
The frequency response changes

Question 30

How can the frequency response problem be overcome

Answer 30

Using a voltage follower circuit. The RC components are isolated from the next stage in the system. There is little to no current. It transfers voltage and there is a high input resistance

Question 31

Draw a voltage follower circuit

Answer 31

See in notes for diagram

Question 32

Give the break frequency equation. Not given in the exam

Answer 32

fb=1/2πRC

Question 33

What do inductors do?

Answer 33

Inductors limit AC in a way that resembles behaviour of resistors in DC

Question 34

What units is inductance measured in

Answer 34

Henry

Question 35

Give the equation for inductive reactance

Answer 35

2πfL

Question 36

What does the graph of reactance against frequency for an inductor look like

Answer 36

Straight line through origin

Question 37

If both graphs of capacitive reactance and inductive reactance are drawn together, how would the resonant frequency be calculated

Answer 37

The point where both graphs meet

Question 38

Draw a resonant filter circuit

Answer 38

See notes for details

Question 39

Draw the frequency response graph

Answer 39

See notes fo details

Question 40

How would you calculate Q factor and bandwidth from a frequency response filter graph

Answer 40

Find the break frequency by using the peak voltage gain.
Then calculate 70% of the peak amplitude and mark the 2 points on the graph. The frequency between them is the bandwidth.
To calculate Q factor. Just use the equation
Q=f0/bandwidth

Question 41

State the differences between the ideal frequency response and the practical frequency response

Answer 41

For an ideal frequency response, there is a vertical cut off at the bandwidth. However, the practical frequency response has voltage gain decrease slowly over a range of frequencies

Question 42

Draw a band pass filter circuit

Answer 42

See in notes for answer

Question 43

State the voltage divider in terms of the band pass filter

Answer 43

V0=VinxRd/Rd+R
Rd=Dynamic resistance

Question 44

What does it mean for a filter if the Q factor/Selectivity is high?

Answer 44

It means that its a good filter.

Question 45

What does a high Q factor do to the shape of a frequency response graph

Answer 45

The higher the filter the sharper the frequency response graph.