Chapter 4: Ac circuits and Passive filters Flashcards
What is bandwidth?
The range of frequencies required to make up a signal
What is the bandwidth if the signal is a sine wave?
zero
What is the bandwidth if the signal is a square wave?
infinite-infinite series of sine waves
What is a passive filter?
They are made from combinations of resistors, capacitors and inductors. They can suppress certain frequencies within a frequency spectrum.
What does a low pass filter do?
Low pass filter allows low frequency signals to pass through unaffected but blocks high frequency signals
What does a high pass filter do?
Allows high frequency signals to pass through unaffected but blocks low frequency signals
What does a band filter do?
Only allows a certain ‘band’ of frequencies to pass through unaffected. Any signal higher or lower than the band is blocked
In AC circuits, capacitors don’t have resistance but ________.
Reactance
Give the symbol for capacitive reactance
Xc
Give the equation for capacitive reactance
Xc=1/2πfC
What is reactance measured in?
Ohms
What does the graph of reactance against frequency look like
negative curve due to the 1/
What is impedance?
The combined effect of resistance and reactance
Give the equation for impedance
Z=√R²+Xc²
Z=impedance
Units=Ohms
Draw a low pass filter circuit
Look at notes for diagram. Positive and negative rails in parallel.
R on the positive. Connection from positive to negative. Capacitor on the connection.
State the voltage divider equation in terms of a low pass filter
Vout=Vin/Z x Xc
How to calculate the voltage gain for a low pass filter?
Xc/Z or Vout/Vin
At a low frequency what does the voltage divider for a low pass filter change to
xc²»R²
R² is negligible compared to Xc² so it is ignored
Xc/√Xc² =1
At a high frequency what does the voltage divider for a low pass filter change to
R²»Xc²
Xc² is negligible compared to R²
Vout=Xc/2πfC
What is the break frequency?
When Xc=R
How to calculate Vout at the break frequency
Vout≈0.7 x Vin
On log paper, where is the break frequency
At 45 degrees
Draw a High pass filter circuit
Look at notes for diagram. Positive and negative rails in parallel.
C on the positive. Connection from positive to negative. Resistor on the connection.
Give the potential divider equation in terms of a high pass filter circuit
V0=Vin/Z x R
How to calculate the voltage gain for a high pass filter?
Vgain=R/Z
At a high frequency what does the voltage divider for a high pass filter change to
R²»Xc²
So Vout=Vin/R
At a low frequency what does the voltage divider equation for a high pass filter change to
Xc²»R²
R² is negligble
So Vout=Vin/Xc x R
How to calculate voltage gain of a high pass filter at low frequency
2πfC
What problem arises when connecting a filter output to the next stage in a system?
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
How can the frequency response problem be overcome
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
Draw a voltage follower circuit
See in notes for diagram
Give the break frequency equation. Not given in the exam
fb=1/2πRC
What do inductors do?
Inductors limit AC in a way that resembles behaviour of resistors in DC
What units is inductance measured in
Henry
Give the equation for inductive reactance
2πfL
What does the graph of reactance against frequency for an inductor look like
Straight line through origin
If both graphs of capacitive reactance and inductive reactance are drawn together, how would the resonant frequency be calculated
The point where both graphs meet
Draw a resonant filter circuit
See notes for details
Draw the frequency response graph
See notes fo details
How would you calculate Q factor and bandwidth from a frequency response filter graph
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
State the differences between the ideal frequency response and the practical frequency response
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
Draw a band pass filter circuit
See in notes for answer
State the voltage divider in terms of the band pass filter
V0=VinxRd/Rd+R
Rd=Dynamic resistance
What does it mean for a filter if the Q factor/Selectivity is high?
It means that its a good filter.
What does a high Q factor do to the shape of a frequency response graph
The higher the filter the sharper the frequency response graph.
