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Capacitors
BITX20 bidirectional SSB transceiver
A BITX20 single stage
A simplified single stage
+12 V
R1
R2
0V
A simplified single stage with capacitors
+12 V
R1
C4
C3
R2
0V
C2
C1
Illustrated applications of capacitors
•
Power supply decoupling:
See capacitor C1
•
Signal decoupling:
See capacitor C2
•
Signal coupling:
See capacitors C3 and C4
Some other applications of capacitors
•
RC Filters: See later
•
Tuned circuits: In another talk
(We need to discuss inductors first)
Fields
•
Electric fields
–
•
Magnetic Fields
–
•
Capacitors
Inductors
Electromagnetic (EM) fields
–
–
–
Radio waves
Antennas
Cables
Capacitors
Discharge of a capacitor
Switch
Vout
+10 V
+
R
0V
C
Graph of capacitor discharge from 10V
R=1 Ohm, C=1 Farad
(or R=1 M Ohm, C=1 uF)
Volts
10
8
6
4
2
0.5
1
1.5
2
Seconds
The same discharge from 27.18V
Volts
25
e=2.718
10*2.718
20
15
10
10
5
10/2.718
0.5
1
1.5
2
Seconds
Exponential decay
The RC decay time constant = R times C
If R is in Ohms and C in farads the time is in seconds
Every time constant the voltage decays by the ratio of 2.718
This keeps on happening (till its lost in the noise)
This ratio 2.718 is called “e”.
Exponential decay
It’s a smooth curve. We can work out the voltage at any
moment.
The voltage at any time t is: V
= V0 / e (t/RC)
V0 is the voltage at time zero.
t/RC is the fractional number of decay time constants
For e( ) you can use the ex key on your calculator
Low pass RC filter
R
Vout
Vin
C
0V
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V square wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
2.5
2.5
5
7.5
10
5
7.5
10
12.5
15
Seconds
RC = 1 second
Vin = +/-10V sine wave
Volts
10
7.5
5
2.5
0.2
2.5
5
7.5
10
0.4
0.6
0.8
1
Seconds
What can we say about the phase?
The voltage across a resistor is always in phase with the
current through it
The voltage across a capacitor lags the current through it by 90
degrees
So in an RC series circuit the phases of the R and C voltages
are 90 degrees different.
Our low pass RC filter
R
Vout
Vin
C
0V
What can we say about the amplitude?
The higher the frequency the more current is needed to charge
and discharge a capacitor to the same voltage.
(Ignoring phase) we could say it has less resistance the higher
the frequency. This is what we call impedance.
The impedance of a capacitor in Ohms is 1/(2Pi*f*C)
Where f is the frequency in Hertz and C the capacitance in
Farads.
(2Pi*f is also known as the frequency in radians per second w)
Vector diagram for the low pass Filter
Leading
Lagging
So Vout lags (Vin-Vout) by
90 degrees.
Vin-Vout
(R)
Vin
So we can calculate the filter
output using Pythagoras
90
Vout
(C)
As the frequency increases
Vout moves round the circle
from the top to the bottom
on the right
Vector diagram for the low pass Filter
Leading
Lagging
Vin-Vout
(R)
Vin
90
Vout
(C)
This diagram shows the
corner frequency of the
filter.
This is the 3dB down point
and the phase lag is 45
degrees
This happens when the
impedance of R and C are
the same.
R = 1/(2Pi*f*C).
Low pass gain against frequency
Gain
1
0.8
0.707
0.6
0.4
0.2
0.5
1
1.5
2
2.5
3
2Pi f RC
Low pass phase against frequency
Phase
0.5
1
1.5
2
2.5
3
2Pi f RC
20
40
60
80
-45
High pass RC filter
Vout
Vin
C
R
0V
Vector diagram for the high pass Filter
Leading
Vin-Vout
(C)
Lagging
So Vout leads (Vin-Vout) by
90 degrees.
Vin
So we can calculate the filter
output using Pythagoras
90
Vout
(R)
As the frequency increases
Vout moves round the circle
from the bottom to the top
on the left
Our simplified single stage with capacitors
+12 V
R1
C4
C3
R2
0V
C2
C1
Questions?