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Chelmsford Amateur Radio Society Advanced Course (3) Technical Aspects Part-4 - AC Circuits

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

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Chelmsford Amateur Radio Society Advanced Course (3) Technical Aspects Part-4 - AC Circuits

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  1. Chelmsford Amateur Radio Society Advanced Course(3) Technical AspectsPart-4 - AC Circuits

  2. +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 • As the coil rotates, the Output is a Sine Wave

  3. Amplitude Time One Cycle 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 to1/f, where f is in Hertz • Frequency, f = 1 / T or Period, T = 1 / f

  4. Vmax 270° 90° 0° Time Vmin 360° 180° 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

  5. Vpeak Vrms Time One Period, T 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

  6. Phasor Diagram V I V R F, Hz AC with Pure Resistance • Voltage and Current are in Phase • Standard Ohms Law Applies

  7. I V L Phasor Diagram V F, Hz I AC with Pure Inductance • 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 = 2FL = LNote:  is just common shorthand for 2F

  8. I C V I F, Hz Phasor Diagram V AC with Pure Capacitance • 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

  9. L V VL R V IL VR 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 • 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

  10. VR I R C V VC V Resistance & Capacitance in Series • 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/(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 = ( R2 + XC2)

  11. C R L V Tuned CircuitsSeries Resonance 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

  12. C L R V F, Hz IR IC IL 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.

  13. 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 = 2FL / Ror Q = IXC / IR = 1/ 2FCR • Q can be constrained by the inductance as good quality capacitors have very little loss.

  14. L RD r C V 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 RD=L/(C.r) • 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.

  15. 1.0V 0dB -3dB 0.707V f2 f1 f0 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: Q = f0 / (f2 - f1)

  16. -6dB -60dB 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. Shape Factor is defined as: Bandwidth at -6dB Bandwidth at -60 dB

  17. 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. L Equivalent Circuit Circuit Symbol C1 R C2 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.

  19. Low Pass Amplitude Amplitude Frequency Frequency PI Section T Section High Pass PI Section T Section Filters

  20. PI Section T Section Amplitude Frequency Band Pass Filters • 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.

  21. L Vin Vout C C L Vin Vout 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.

  22. Notch Filter Response 0 Frequency Stop Band Pass Band Loss Loss (dB) 10 Pass Band Pass Band 20 fc

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