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Chelmsford Amateur Radio Society
Advanced Course
(3) Technical Aspects
Part-2 - Resistors and Capacitors
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
1
Voltage Drop
• In any closed circuit if current is flowing there must be a
voltage drop across circuit elements.
• This follows OHMS LAW which is recalled as:-
R=V/I
Chelmsford Amateur Radio Society
Advanced Licence Course
V=I.R
Carl Thomson G3PEM
I = V /R
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
2
Source Resistance
• There is NO ideal source.
• Every source has some internal resistance.
• This is termed Source Resistance/Impedance.
• When current is drawn there is a voltage drop across this
internal resistance/impedance
• Source resistance limits the amount of power that can be drawn.
Example: Lead Acid cells have very low internal resistance
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
3
ElectroMotive Force - EMF
• EMF is the unloaded potential difference between two points.
• The electromotive force of a source is that force which tends to cause a
movement of electricity in a circuit.
• It has an unloaded voltage V which can be transposed to the output
terminals provided no current flows.
Internal
Resistance, r
EMF
Source, V
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
4
Potential Difference
• The loaded voltage is the Potential Difference between two points
when current is flowing in the circuit.
Internal
Resistance, r
Potential
Difference
Load, R
Source, V
• There is now a potential difference across the load as current is
flowing. The value of which follows Ohm's Law.
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
5
Resistors in Series/Parallel
•
Resistors in Series:-
Rtotal = R1+ R2+ R3 . . .
R1
•
R2
R3
Resistors in Parallel:-
1/Rtotal = 1/R1+1/R2+1/R3 . . .
R1
R2
R3
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
6
DC Power
Internal
Resistance, r
Power, P in Load = V x I
Source
• Power is measured in WATTS.
• The calculation for power in a circuit is Volts multiplied by Amps
P=V.I
and also
P = I2 x R
P = V2 / R
from using Ohms Law for V or I
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
7
Potential Dividers
• By connecting resistors in series a potential divider network can
be constructed. This is the basis of Volume controls, trimmers etc
VIN
R1
10v
R2
VOUT
• VOUT can be calculated by proportion without worrying about the
current through the resistors if load is high impedance at VOUT.
VOUT = VIN x R2 / ( R1 + R2 )
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
8
Safety Leakage Paths
• Capacitors can hold a lethal charge when open circuit.
• A parallel resistor can provide a safety leakage path to discharge large
value capacitors.
• High value resistors provide a very low current drain across a capacitor.
For example it can make a PSU safer without affecting operation.
• In a circuit this is known as a BLEED RESISTOR.
Bleed Resistor
Value greater
than 100K
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
9
Capacitance
• Potential difference between A & B. Charge is set in
motion therefore current flows.
• The amount of current is determined by the nature of
the conductor - its Resistance
A
+
B
• Also a potential difference between A & B, but other
than the short time at switch-on NO current will flow.
• However the negative plate will contain an excess of
electrons and the positive plate a deficit.
+
-
A
B
• The plates are said to be charged and the name given
to the ability to store charge is Capacitance.
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
10
Capacitors
• Instead of two ends of wire a capacitor is made up of two or more flat
parallel plates. The capacitance can be calculated.
Dielectric
Metal Plates, Area “A”
Spacing "d"
• The plates have area "A" and are separated by distance "d".
• The space between the plates is filled with an insulating material known
as the DIELECTRIC
• Dielectric can be any insulator - typically Oxides, Plastics, or Ceramic
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
11
Capacitance & Charge
• The Unit of Capacitance is the FARAD [after Faraday]
• A capacitance of 1 FARAD is when 1 Coulomb of charge is stored
with 1 Volt PD.
Q = C.V
or
Q/C=V
or
Q/V=C
• One Farad is rather large so uF, nF, pF are more common
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
12
Capacitors
•
CAPACITANCE, C is :
– Proportional to the plate area "A".
– Inversely proportional to the distance between the plates "d”
– Depends upon the material used for the dielectric.
•
This can be written as C = 0 r A / d where
C
is in Farads
A
is area of each plate in square metres
d
is distance between plates in metres.
• ε0
• εr
ε ε
- A constant known as the permittivity of free space
[or vacuum, dry air] having a value of 8.854 x 10-12 .
- [or “k”] Relative permittivity of the dielectric, chosen for
its TEMPERATURE STABILITY, BREAKDOWN VOLTAGE
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
13
Capacitance Formula &
Dielectric Materials
The formula
C = ε0 εr A / d
C=K.A/d
is also written as
where
K = ε0 εr
• The dielectric type in a capacitor will depend upon the function the
capacitor is to perform in a circuit.
• As frequency increases dielectric loss increases,
• Each dielectric also has different breakdown voltages.
• Each material will suffer a change in properties due to temperature, this
will affect the capacity.
• Typical εr - Air=1, PTFE=2, Mica=5, ceramics ~10, Hi-k ceramics ~10000
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
14
Capacitors in Parallel
• Capacitors connected in parallel all have the same voltage
• The charge on them is dependent upon the capacitor value.
C1
C2
C3
V
Ctotal = C1 + C2 + C3
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
15
Capacitors in Series
• When capacitors are in series the charge is the same in all of the circuit
• The voltage is divided between capacitors.
C1
C2
C3
V
1/Ctotal = 1/C1 + 1/C2 + 1/C3
Chelmsford Amateur Radio Society
Advanced Licence Course
Carl Thomson G3PEM
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
16
Charge & Discharge
of a Capacitor
1
R
2
C
Voltage, V
VC
I
Discharging
VC
Charging
t
I
Chelmsford Amateur Radio Society
Advanced Licence Course
Time = C.R Secs.
Where
C = Farads
R = Ohms
Carl Thomson G3PEM
VC
t
I
Slide Set 2: v1.0, 29-Aug-2004
(3) Technical Aspects - Rs and Cs
17