chelmsford amateur radio society advanced course (3) technical aspects part-4 - ac circuits
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Chelmsford Amateur Radio Society Advanced Course (3) Technical Aspects Part-4 - AC Circuits. +V. Time. N. S. -V. Slipring. Brush. AC Volts Output. One Rotation. AC Generation. Consider a rotating coil in a magnetic field Voltage is induced when the ‘magnetic flux’ lines are cut - PowerPoint PPT PresentationTRANSCRIPT
1Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Chelmsford Amateur Radio Chelmsford Amateur Radio Society Society
Advanced CourseAdvanced Course(3) Technical Aspects(3) Technical Aspects
Part-4 - AC CircuitsPart-4 - AC Circuits
2Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
AC Generation
• Consider a rotating coil in a magnetic field
• Voltage is induced when the ‘magnetic flux’ lines are cut
• As the coil rotates, the Output is a Sine Wave
+V
Time
One Rotation
-V
N S
AC Volts OutputBrush
Slipring
3Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Period & Frequency
• In the last courses we just described the shape of a sine wave
• The Period, T of one cycle, in seconds is equal to 1/f, where f is in Hertz
Frequency, f = 1 / T or Period, T = 1 / f
Amplitude
Time
One Cycle
4Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Phase
• Another way of looking at the sine wave is as a cycle of 360 degrees
• The voltage or current has a complete rotation as in the generator;
• This indicates the phase of the signal at any part of the cycle
• Phase difference can be used to describe the delay between two signals.
• Phasor diagrams also describe the phase difference - See Handbook
180° 360°
0°
Vmax
Vmin
90°
270°
Time
5Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
R.M.S. Value
• RMS = Root Mean Square
• The RMS value of any varying shaped waveform is the equivalent of the constant DC Voltage that would have the same power or heating effect
• For a sine wave, the RMS value is equal to 1/2 of the peak value.
Vrms = 0.707 . Vpeak and Irms = 0.707 . Ipeak
Vpeak
Vrms
Time
One Period, T
6Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
AC with Pure Resistance
RF, Hz
VPhasor Diagram
V I
• Voltage and Current are in Phase• Standard Ohms Law Applies
7Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
AC with Pure Inductance
Phasor DiagramV
I
• THE CURRENT LAGS 90° BEHIND THE VOLTAGE• The magnitude of the current depends upon;
a) the inductanceb) the frequency of the applied ac current.
• These two factors influence the Back EMF.• The current, I equals Volts divided by L - a form of Ohms law• This unusual form of conductor resistance is the opposition due to the
Back EMF and is known as REACTANCE and given the symbol XL
XL = 2FL = L Note: is just common shorthand for 2F
L
F, Hz
VI
8Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
AC with Pure Capacitance
I
V
Phasor Diagram
• The CAPACITIVE REACTANCE is the ratio of voltage to current
V / I = Xc = 1/(2.F.C) = 1/(.C)
• So the Current LEADS the Voltage by 90°
• Reactance and therefore the current is dependent upon the frequency as well as the C or L
Remember the word: CIVIL
C
F, Hz
VI
9Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Resistance & Inductance in Series
• Impedance is the vector sum of the resistance and reactance.
• A definition is the ratio of the RMS EMF in a circuit, to the RMS current
VLV
VR
IL
• R represents the 'total' circuit resistance.
• The Voltage is made up of two parts; a PD across the resistance VR with the voltage and current in phase, and a PD across the inductance VL leading the current by 90°.
• The resultant is the applied voltage V, which is the vector sum given by:-
• Impedance, Z = ( R2 + XL2) The current in the circuit is I = V / Z
RL
V
10Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Resistance & Capacitance in Series
I
V
VR
VC
• To maintain a current of I the applied voltage provides two components;a) A voltage VR = I.R across the resistance, in phase with the current, and
b) A voltage VC = I.C = I.1/(2FC) which lags the current by 90°.
• The resultant is V which is the vector sum of these two components.
• The impedance of the circuit is Z = ( R2 + XC2 )
R C
V
11Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Tuned CircuitsSeries Resonance
• The applied voltage has three components;VR = IR across R and in phase with the current I
VL = I.L across the inductance and leading the current by 90°
VC = I.1 /C across the capacitance and lagging the current by 90°
• VL and VC being 180° out of phase.
• At resonance VL = VC therefore I.L = I.1 /C so XL = XC
• The particular frequency when XL = XC is known as the resonant frequency
• The formula is F = 1 / LC or F = 1 / 2(LC) or in terms of • L = 1 / 4 2 F2 C or in terms of C = 1 / 4 2 F2 L
The series resonant circuit gives maximum current and minimum impedance at resonance and is known as an acceptor circuit
R CL
V
12Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Tuned CircuitParallel Resonance
The active current has three components;
• IR = V / R in phase with the voltage.
• IC = CV which leads the voltage by 90°
• IL = V / L which lags the voltage by 90°
When we consider IL = IC then V / L = CV • F = 1 / 2 LC or alternatively . . .• L = 1 / 4 2 F2 C or C = 1 / 4 2 F2 L
• A parallel circuit tuned to resonance is known as a rejector circuit.
• It offers maximum impedance to the resonant frequency.
• At resonance the supply current, I = IL - IC and as they are equal and thus are zero, the impedance Z = V / I = V / 0
• Thus impedance is infinitely great. In practice the R modifies this.
LC
F, Hz
V R
IR IC IL
13Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Magnification Factor ‘Q’
• At resonance the voltage across the inductance or capacitance can be several times greater than that supplied.
• The current is determined by the value of R but the voltage across the circuit is determined by the current multiplied by the reactance.
• This gives a voltage greater than that applied.
• The ratio of the volts across the resistor to that across the reactance is called the Magnification factor, Q.
• If the current at resonance is I for the inductance:
Q = IXL / IR = 2FL / R or Q = IXC / IR = 1/ 2FCR
• Q can be constrained by the inductance as good quality capacitors have very little loss.
14Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Dynamic Resistance
• Practical Parallel Tuned circuits do not have infinite impedance at resonance due the finite resistance, r of the Inductor
• The effective value of the impedance of a parallel tuned circuit at resonance is called the Dynamic Resistance, RD
• For a high RD the ratio of L to C should be high and r small.
• Note: If a resistance is connected in parallel with RD then the circuit is damped and the Q is lowered - used to shape the response of tuned circuits in amplifiers.
r
C
L
V
RD RD=L/(C.r)
15Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Bandwidth
• Bandwidth is defined as the width of the resonance curve at a specified point from the peak, normally at 3 dB down.
• Note that for 3dB down from the peak, decibel calculations give this as the ½ power point, or 1/2 which is 0.707 of the peak value.
• The bandwidth can be altered by changing the Q of the circuit, eg damping resistors value or if coupling factors.
• Bandwidth is also be related to Q:
-3dB
0dB
f0 f2f1
0.707V
1.0V
Q = f0 / (f2 - f1)
16Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Shape Factor
• Shape Factor: Resonant and Filter responses have a shape to them
• The better the shape factor the better the rejection of unwanted signals.
-6dB
-60dB
Shape Factor is defined as: Bandwidth at -6dB Bandwidth at -60 dB
17Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Circulating Currents
Parallel Tuned Circuits
• These have high impedance and low current across the circuit
• Internally within the tuned circuit the current sees a series circuit and therefore a low impedance
• This can cause very high currents and the danger of over heating.
Series Tuned Circuits
• Because of the high reactance's the voltage can be very high,though with relatively little current present.
18Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Quartz Crystals
• Quartz is natural material which vibrates due to the piezo-electric effect
• Quartz Crystals are slabs of quartz clamped between two metal plates.
• They are equivalent to a series tuned circuit with a very high Q
• There is also a parallel circuit, C2.
• The series resonance is a low impedance acceptor circuit and the parallel resonance is a high impedance rejector circuit.
Circuit Symbol C1
C2
R
LEquivalent Circuit
19Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Filters
Amplitude
Frequency
Amplitude
Frequency
Low Pass
PI Section T Section
High Pass
PI Section T Section
20Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Band Pass Filters
Amplitude
Frequency
Crystal Filters
• Quartz Crystals can be configured to form a half lattice filter.
• Two crystals are chosen so their frequencies differ by the amount of bandwidth required.
T Section PI Section
21Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Band Stop / Notch Filters
Series LC to Ground
• Low Impedance at resonance
• Stops a given band of frequenciesat resonance.
• Passes others outside of resonance
Parallel LC in Signal Path
• High Impedance at resonance
• Blocks the unwanted signal
• Passes others outside of resonance
Notch Filter
• When response is sharp they are callednotch filters removing a spot frequency.
VoutVinL
C
VoutVinL
C
22Chelmsford Amateur Radio SocietyAdvanced Licence Course
Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006(3) Technical Aspects - AC Circuits
Notch Filter Response
Frequency
0
Pass Band
Stop Band
Pass Band
fc
Pass Band Loss
10
20
Loss (dB)