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ANADOLU UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EEM 206 ELECTRICAL CIRCUITS LABORATORY EXPERIMENT#3 RESONANT CIRCUITS 1 RESONANT CIRCUITS The resonant circuits are used to select or reject specific bands or frequencies. The band may be narrow or broad. TV, radios, and other types of transmitting and receiving equipment to select the broadcast or receiving frequency use them Modern communications would be impossible without the use of resonant circuits Resonant circuits consist of inductance and capacitance. The Series Tuned Circuits If a series resonant circuit is wired into the circuit as seen in figure 1, only the desired signal is passed on into the load. Figure 1 can be called a "band-pass" filter since it tunes in a specific frequency and eliminates all others. Figure1: A series resonart circuit, in series with the signal line allows only a narrow band of frequencies to be used by the load. However, if placed into circuit as seen in figure 2, a frequency (actually, a narrow band of frequencies) is shunted to ground. Figure 2 is a "trap" because it traps out unwanted signals and sends them to the ground. Figure2: A series resonant circuit, parallel with the signal line, allows all but a narrow band of frequencies to enter the load. 2 The resonant frequency is found by the formula: fr = 1 2π LC Where fr is the resonant frequency, L is inductance in henrys, C is capacitance in farads. At this frequency XL will equal XC and the lowest possible circuit impedance results. Broadband curve Narrow band curve Figure 3: Series resonant circuit frequency response charecteristics. Figure 3 shows a graph of the frequency response characteristic of resonant circuit. We can have the circuit respond to a broad band or narrow band frequencies. There are uses for both. The TV channel is 6 MHz wide in order to contain the picture, sound, and color information. A broad-band circuit is necessary to pass all these frequencies. In AM radio you only want a signal station to be received so narrow-band tuning is required. The Q of a resonant circuit is its "Figure of merit" indicating a ratio of XL to R. Mathematically, Q=XL/R. When XL is high and R of the coil is low, the Q is high and tuning is sharp (narrow bandwidth). When XL is low and R is high, the opposite is true. It can be seen that additional R causes the bandwidth to increase. Mathematically, bandwidth is defined as being BW= fr/Q where fr, is the resonant frequency and Q is the quality figure for the circuit. The Parallel Tuned Circuits The parallel resonant circuit has high impedance at the resonant frequency. Figure 4 illustrates why this is true. Note that as applied frequency increases, XL also increases. But XC decreases. This means that a low impedance path to the ground exists through C. The opposite is true if the applied frequency is lower than fr. Only when XL is equal to XC there is a high impedance both legs of the parallel circuit. 3 XC XL Volts 0 Frequency Figure 4: Reactance curves-fr is the frequency where XC and XL curves cross. To trap out unwanted signals the parallel circuit is connected in series with the signal line as seen in Figure 5. To tune out a single signal from a group of signals, the parallel circuit is placed with the signal line. At resonance the fr sees a high impedance to ground. In figure 6, so it goes to the load for use. All other frequencies have a low impedance to ground and never used by the load. Figure 5: A “parallel-wired ” tuned circuit passes all but fr to ground, allowing only fr to be applied to the load. Other theories of resonat circuits: Q, bandwidth and fr, are same as for series circuits. Formulas are the same: BW = fr Q Q= XL R fr = 1 . 2π LC Figure 6: A “series-wired” parallel tuned circuit “traps out” unwanted signals and lets all others pass. 4 EXPERIMENTAL WORK PART-A SERIES TUNED CIRCUlT Materials Required: 1) Frequency Counter (if possible) or scope 2) A D.C power supply and board 3) DMM 4) Resistors, 470 ohm ¼ watt 5) Inductor 25 mH 6) Capacitor 1, 0.01 µF, 25 volts. Procedure: 1. Connect the circuit shown in figure 7. 2. Calculate the circuits' fr. 3. Observe the RMS voltage across the capacitor. Vary the generator frequency to each side of your calculated fr until Vc is maximum. This is the actual fr. 4. Go below and above fr in 500 Hz steps. Measure the VC at each step and record it. Do this for each 500 Hz step from fr to fr+3000 Hz and fr-3000 Hz. If you can maintain the input signal level at a fixed value, you can make note of the 10 % points and calculate the bandwidth. 5. Draw a frequency response curve for your circuit. 6. Place the 470 ohm resistor in series with the coil. Repeat steps 4 and 5. Function Generator Sine Freq.counter or scope R* = 25 mH V * Coil “wire resistance” depends on coil used-measure with ohmmeter (Or scope) Figure 7 5 PART-B PARALLEL TUNED CIRCUlT Materials Required: 1) 2) 3) 4) 5) Oscilloscope or DMM A D.C power supply and board Resistor 100 KΩ ¼ watt Inductor 25 mH Capacitor 0.01 µF, 25 volts. Procedure: 1. Connect the circuit shown in figure 8. 2. Calculate the circuits' fr. 3. Set the generator at the calculated fr. 4. Adjust the generator frequency above and below the calculated fr until the scope shows minimum V. This is the actual circuit fr. 5. Go below and above fr in 500 Hz steps. Measure V at each 500 Hz interval and record it. Do this for each interval up to 3000 Hz above fr and down to 3000 Hz below fr. 6. Draw a frequency response curve for your circuit. Function Generator Sine 20-35 mH 10 K Scope Figure 8 6