Experiment 8: LORD Circuit Aim The aim of this experiment is to measure and calculate the resonance frequency in different ways. Meanwhile, there is a requirement to use the apparatus proficiently. For the last part of the experiment, there is a demand to analyze the phenomenon and get better understanding. Moreover, from this experiment, we can understand the principle Of this experiment and learn some circuit knowledge. Background/ Theory In the experiment, in an LORD circuit, a resistor(R), an inductor (L) and a capacitor (C) are required to connect in series.

Just like the figure shows. In he experiment, we want to calculate the resonance frequency. We know the current will be maximum when the circuit is driven at its resonance frequency. In addition, the amplitude 10 of the AC current in a series LORD circuit depends on the amplitude VOW of the applied voltage and the impedance Z, which is a measure tot the overall opposition tot a circuit to the flow tot an electrical current as , So we just need to use the apparatus to measure the maximum voltage.

As we know, at the resonance truculence, we have XSL-XX and the impedance, Z is equal to the resistance R, where Z=R, Because the capacitive and inductive reactants ray with the frequency of the AC current, the impedance of a circuit containing capacitors and inductors also varies with AC frequency. For a circuit with AC current flowing at angular frequency w, its impedance is given by where XSL = WALL is the inductive reactant, XX = I/OIC is the capacitive reactant, R is the resistance, and = an f (f is the linear frequency).

Apparatus ; PC With Auditions installed ; Science Workshop 750 USB Interface Box ; Power Amplifier ; Voltage Sensor ; AC/DC Electronics Lab Board ; LLC meter ; Connecting patch cords Experimental Procedure The experimental procedure can be divided into three parts: Part l: Using a Frequency Scan to Determine the Resonance Frequency ; The first step was to check all the apparatus were there and well. ; The Power Amplifier was connected to Analog Channel A and Voltage sensor was connected to Analog Channel B of the Science Workshop 750 LIST Interface Box. The Signal Output Of the Power Amplifier was connected to the it,VOW banana jacks on the AC/DC Electronics Lab Board and the banana plug patch cords that provided are used to connect. ; Prepare a 10 resistor, a 100 capacitor and the inductor. They were unconnected with the Power Amplifier in series on the AC}DC Electronics Lab Board as shown in the figure. ; Analog sensors was accurately added to Channel A and B into Auditions which was in the computer and set up appropriately. The following settings were used for the signal generator: ; Output: Sine Wave. Amplitude: 3. 0 V. ; Frequency: 10 Hz’s, ; Increment factor: 10. ; In the same Scope display, both Voltage Channel g and Output Voltage were added as measured quantities versus time. And the graph was observed. ; Through the graph, the amplitude of the voltage across the resistor was easily baserВ»De and determined. ; The frequency was changed from 10. Hz’s to 270 Hz’s to repeat the measurement in order to find the resonance frequency, ; The 4/ if and 330 if capacitor was changed to repeat the experimental procedures in order to find their own resonance frequencies ; The resonance frequencies of the capacitors were determined by the Frequency Scan as required. Part II: using a Phase Portrait to Determine the Resonance Frequency ; The LLC Meter was set to Inductance to measure and record the inductance Of the inductor. ; The LLC Meter was set to Capacitance to measure and record the capacitances Of the 47 pug. 00 330 capacitors.

And different numerical values were recorded. ; The apparatus was set up on the AC}DC Electronics Lab Board in series as shown in the figure. ; The Scope display was used to monitor Voltage Channel B. And the x. Axis was changed to measure Output Voltage. ; The approximate resonance frequency was estimated and used for the capacitor used as the signal generator frequency. ; The frequency was changed slowly to adjust until a relative straight line plot of Voltage Channel B vs. Output Voltage was obtained, which meant that the output voltage and the voltage across the resistor were in phase. The relatively accurate resonance frequency was recorded. ; The experimental procedures were repeated for all the 3 capacitors and the results were recorded, part Ill: Measurement of peak Voltages at Resonance ; The apparatus was set up on the AC/DC Electronics Lab Board in series as shown in the figure. ; The Scope display of the Auditions was set up. ; The peak voltage across each component of the circuit was measured at resonance frequency by using the Scope display and Voltage Sensor. ; The experimental procedures were repeated for all the 3 capacitors and the results ere recorded.

Results 1. The amplitudes of the voltage across the resistor for different frequencies and capacitors: The frequency that is corresponding to the peak current is the resonance frequency. So we can easily get the resonance frequency from the graph: puff 250 Hz’s puff 185 Hz’s 3301* 98 Hz’s 2. The true values of the three capacitors by measurement: capacitors 147 if Coif 1 puff I Measurement | 49. 49 As we can see in the figure, the true values of the capacitors are different from the standards. The reason may be that after a long time using, the capacitances changed.

So when we calculate the resonance frequency by using the equation: we should use the true values instead of the standards. And and from measurement the inductance of the inductor is 8. 110 mm, So we can calculate the resonance frequencies: capacitors 147 if 1 I Resonance Frequencies | 251. 2 Hz’s 186. 1 Hz’s 96. 4 Hz’s I 3. The resonance frequencies of the three capacitors by using the phase portrait: capacitors 147 100 if 1 I Resonance Frequencies | 251 Hz’s 186 Hz’s 1 GHz I Compared to the calculation, the results were quite accurate. 4. The peak voltages for each component of three capacitors in the last part:

Capacitors I peak Voltages for R peak Voltage for C I peak Voltage for L I Total voltages 47 IF 1. 691 V 1 2. KICK. ‘ 2. IV 6. KICK,’ I | 5121 v I 330 1. Iv | 0. 971 v 1 1. KICK. ‘ 4. Iv All the total voltages are bigger than the amplitude voltage provided by the Power Amplifier Discussion and Analysis Discussion 1: The experimental error In this experiment, there are several errors. The first one is the resistance of the resistor. The resistance that is given is Ion. But after a long time using, the resistance Will change, and not 100, Which can affect the result. The second one is the numerical reading.

In this experiment, we should read the frequency numbers in the computer, Which can result an error. Moreover, the lead can affect the whole circuit. As we know, lead also has resistance, which can affect the results. But the experimental error is not very important in this experiment overall and it only affects the results slightly. Discussion 2: The voltage As we can see in the form 4 of the Result Part, all the total voltages are bigger than the amplitude voltage provided by the Power Amplifier—-3 V. It seemed strange but actually it was right. Suppose us is the input voltage provided by the

Power Amplifier and LU- is the output voltage. So we can get Where Q is the factor of quality, And when Q is bigger than 1, the output voltage is bigger than input voltage. And the factor tot quality is . From calculating, all the Q are bigger than l, 50 the output voltage is bigger than 3 V. The reason is that the current is flowing between the components. The voltage of each component is changing, And when we measured the peak voltages, we were at different times. As a result, the total is bigger. But we measure all the components at the same time, the total voltage must be 3 V.

Moreover, when the circuit is in resonance, the output voltage is almost bigger than input voltage. But this phenomenon is bad for the component. So we must avoid resonance in the power output system. Discussion 3: The results of resonance frequencies As eve can see from the forms, the resonance frequencies are quite similar, which means the results are quite accurate. We used different ways, but we can get almost the same answer. The reason is that the experimental error is so slight that we can ignore it. And we can see that the bigger the capacitance, the lower the resonance frequency.