1. 1 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits Chelmsford Amateur Radio Society Advanced Course (3) Technical Aspects Part-4 - AC Circuits

2. 2 Chelmsford Amateur Radio Society Advanced 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 NS AC Volts Output Brush Slipring

3. 3 Chelmsford Amateur Radio Society Advanced 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

4. 4 Chelmsford Amateur Radio Society Advanced 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° V max V min 90° 270° Time

5. 5 Chelmsford Amateur Radio Society Advanced 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. V rms = 0.707. V peak and I rms = 0.707. I peak V peak V rms Time One Period, T

6. 6 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits AC with Pure Resistance R F, Hz V Phasor Diagram V I Voltage and Current are in Phase Standard Ohms Law Applies

7. 7 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits AC with Pure Inductance Phasor Diagram V I THE CURRENT LAGS 90° BEHIND THE VOLTAGE The magnitude of the current depends upon; a) the inductance b) 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 X L X L = 2  FL =  L Note:  is just common shorthand for 2  F L F, Hz V I

8. 8 Chelmsford Amateur Radio Society Advanced 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 = X c = 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 V I

9. 9 Chelmsford Amateur Radio Society Advanced 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 VLVL V VRVR ILIL R represents the 'total' circuit resistance. The Voltage is made up of two parts; a PD across the resistance V R with the voltage and current in phase, and a PD across the inductance V L leading the current by 90°. The resultant is the applied voltage V, which is the vector sum given by:- Impedance, Z =  ( R 2 + X L 2 ) The current in the circuit is I = V / Z R L V

10. 10 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits Resistance & Capacitance in Series I V VRVR VCVC To maintain a current of I the applied voltage provides two components; a) A voltage V R = I.R across the resistance, in phase with the current, and b) A voltage V C = I.C = I.1/(2  FC) 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 =  ( R 2 + X C 2 ) RC V

11. 11 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits Tuned Circuits Series Resonance The applied voltage has three components; V R = IR across R and in phase with the current I V L = I.  L across the inductance and leading the current by 90° V C = I.1 /  C across the capacitance and lagging the current by 90° V L and V C being 180° out of phase. At resonance V L = V C therefore I.  L = I.1 /  C so X L = X C The particular frequency when X L = X C 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 F 2 C or in terms of C = 1 / 4  2 F 2 L The series resonant circuit gives maximum current and minimum impedance at resonance and is known as an acceptor circuit R C L V

12. 12 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits Tuned Circuit Parallel Resonance The active current has three components; I R = V / R in phase with the voltage. I C =  CV which leads the voltage by 90° I L = V /  L which lags the voltage by 90° When we consider I L = I C then V /  L =  CV F = 1 / 2  LC or alternatively... L = 1 / 4  2 F 2 C or C = 1 / 4  2 F 2 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 = I L - I C 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. L C F, Hz V R IRIR ICIC ILIL

13. 13 Chelmsford Amateur Radio Society Advanced 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 = IX L / IR = 2  FL / R or Q = IX C / IR = 1/ 2  FCR Q can be constrained by the inductance as good quality capacitors have very little loss.

14. 14 Chelmsford Amateur Radio Society Advanced 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, R D For a high R D the ratio of L to C should be high and r small. Note: If a resistance is connected in parallel with R D then the circuit is damped and the Q is lowered - used to shape the response of tuned circuits in amplifiers. r C L V RDRD R D =L/(C.r)

15. 15 Chelmsford Amateur Radio Society Advanced 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 f0f0 f2f2 f1f1 0.707V 1.0V Q = f 0 / (f 2 - f 1 )

16. 16 Chelmsford Amateur Radio Society Advanced 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

17. 17 Chelmsford Amateur Radio Society Advanced 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.

18. 18 Chelmsford Amateur Radio Society Advanced 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 L Equivalent Circuit

19. 19 Chelmsford Amateur Radio Society Advanced 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 SectionT Section

20. 20 Chelmsford Amateur Radio Society Advanced 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

21. 21 Chelmsford Amateur Radio Society Advanced 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 frequencies at 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 called notch filters removing a spot frequency. V out V in L C V out V in L C

22. 22 Chelmsford Amateur Radio Society Advanced 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 fcfc Pass Band Loss 10 20 Loss (dB)