Transcript Generation
Chelmsford Amateur Radio Society Advanced Course (3) Technical Aspects Part-4 - AC Circuits Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 1 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 N S -V Slipring Brush Chelmsford Amateur Radio Society Advanced Licence Course AC Volts Output Carl Thomson G3PEM One Rotation Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 2 Period & Frequency • In the last courses we just described the shape of a sine wave Amplitude Time One Cycle • The Period, T of one cycle, in seconds is equal to 1/f, where f is in Hertz Frequency, f = 1 / T Chelmsford Amateur Radio Society Advanced Licence Course or Carl Thomson G3PEM Period, T = 1 / f Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 3 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; Vmax 270° 0° 90° Time Vmin 180° 360° • 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 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 4 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 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 5 AC with Pure Resistance Phasor Diagram V R I V F, Hz • Voltage and Current are in Phase • Standard Ohms Law Applies Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 6 AC with Pure Inductance V I V L Phasor Diagram F, Hz 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 XL XL = 2FL = L Note: is just common shorthand for 2F Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 7 AC with Pure Capacitance I V I C Phasor Diagram F, Hz V • 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 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 8 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 L R V VL V 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) Chelmsford Amateur Radio Society Advanced Licence Course The current in the circuit is I = V / Z Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 9 Resistance & Capacitance in Series R VR C I V VC V • 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 Chelmsford Amateur Radio Society Advanced Licence Course Z = ( R2 + XC2 ) Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 10 Tuned Circuits Series Resonance R C L V The series resonant circuit gives maximum current and minimum impedance at resonance and is known as an acceptor circuit • 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 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 11 Tuned Circuit Parallel Resonance V F, Hz R IR L C IC IL 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. Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 12 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. Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 13 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 L r RD C RD=L/(C.r) V • 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. Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 14 Bandwidth • Bandwidth is defined as the width 0dB of the resonance curve at a specified point from the peak, -3dB normally at 3 dB down. 1.0V 0.707V • 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: Chelmsford Amateur Radio Society Advanced Licence Course f1 f0 f2 Q = f0 / (f2 - f1) Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 15 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: Chelmsford Amateur Radio Society Advanced Licence Course Bandwidth at -6dB Bandwidth at -60 dB Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 16 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. Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 17 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 Equivalent Circuit L C1 R C2 Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 18 Filters Low Pass Amplitude PI Section Frequency T Section High Pass Amplitude Frequency PI Section Chelmsford Amateur Radio Society Advanced Licence Course T Section Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 19 Band Pass Filters T Section PI Section 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. Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 20 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 L Vin C 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 Vin notch filters removing a spot frequency. Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Vout C L Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits Vout 21 Notch Filter Response 0 Stop Band Pass Band Loss Loss (dB) 10 20 Pass Band Pass Band Frequency fc Chelmsford Amateur Radio Society Advanced Licence Course Carl Thomson G3PEM Slide Set 4: v1.2, 20-Aug-2006 (3) Technical Aspects - AC Circuits 22