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[...]... between the pass and the stop bands and much more elaborate filter circuits have to be devised Band-pass and band-stop characteristics 18 Electronic and electrical servicing are often plotted on a linear scale of frequency so that the bandwidth is easier to read from the graph, but the attenuation is always plotted in terms of decibels Calculations on such filters are very difficult Standard filter tables... 1/(2πC1R1) Hz and fhf ϭ 1/(2πC2R2) Hz 12 Electronic and electrical servicing and if the stages did not load each other the bandwidth of the circuit would simply be the difference between these two frequencies This is rarely the case for practical values and in effect the high- and low-pass corners are pulled towards each other by the loading effects This type of filter can suffer from quite large in-band insertion...6 Electronic and electrical servicing Practical 26.1 (Continued) Connect a 4.7 μF capacitor between the terminals, and set the signal generator to a frequency of 100 Hz Adjust the output so that readings of a.c voltage and current can be made Find the value of VЈ/IЈ’ at 100 Hz Repeat the measurements at 500 Hz and at 1000 Hz Tabulate values of XC ϭ VЈ/IЈ and of frequency f Now remove the capacitor and. .. characteristics? A circuit that selects a band of frequencies is described as a band-pass filter (BPF) and one such circuit can be constructed as shown in Figure 26.13 This is effectively a cascade of an LPF and an HPF and its attenuation characteristic is shown in Figure 26.13(b) The attenuation slope at both ends is still Ϫ6 dB per octave The two Ϫ3 dB break points of the individual lowand high-pass sections are... reactance at 100 Hz and 1000 Hz as before, and tabulate values of XL ϭ VЈ/IЈ and of frequency f Next, either remove the core from the inductor or increase the size of the gap in the core (if this is possible), and repeat the measurements How has the reactance value been affected by the change? There is another important difference between a resistance and a capacitive or inductive reactance and this can be... Figure 26.8 Series circuits: (a) RLC, and (b) RC circuit for practical example Practical 26.2 Connect the circuit shown in Figure 26.8(b) Use either a highresistance a.c voltmeter or an oscilloscope to measure the voltage VЈ across the resistor and the voltage VЈ across the capacitor Now R C measure the total voltage V and compare it with VЈ ϩ VЈ R C 8 Electronic and electrical servicing The reason why... both the phase and the magnitude of the voltage wave across each component VL VL VL Ϫ VC 2 VR I VR I VR V ϩ( ϪV L )2 C VL Ϫ VC ∅ VR VC VC (a) (b) (c) Figure 26.9 Phasor diagrams for complex series circuits: (a) relationship between V and I for a series RLC circuit, (b) combining VL and VC, and (c) finding the total voltage across the circuit To represent the opposite effects that capacitors and inductors... of R and X known and the angle between them a right angle, the Z line can be drawn in, representing the impedance value of the whole circuit The angle of this line to the horizontal is the phase angle between current and voltage in the circuit Another way of working out the relationships between R, X and Z in a complex circuit is to express them by two algebraic formulae: Z ϭ ( X L Ϫ XC )2 ϩ R 2 and. .. 26.15) The 13 Sine wave driven circuits R1 R1 C2 Vout Vin C1 C1 R2 C2 ϭ 2C1 R2 ϭ 2R1 (a) Vout / Vin 0 dB fc (b) Figure 26.14 Band-stop filter (twin-T): (a) circuit, and (b) typical response XΩ XL XC XL R f Hz (a) Figure 26.15 Resonance in a series LCR circuit XC (b) 14 Electronic and electrical servicing impedance of the circuit will therefore be simply equal to its resistance The same conclusion can be... L is the inductance (henries), C the capacitance (farads), and f is the frequency (hertz) Example: What is the resonant frequency of a circuit containing a 200 mH inductor and a 0.05 mF capacitor? Solution: Substitute the data in the equation, taking care to reduce both L and C to henries and farads, respectively Use L ϭ 200 ϫ 10–3 ϭ 0.2 H and C ϭ 0.05 ϫ 10–6 ϭ 5 ϫ 10–8 F Take 2π as being approximately .