A Circuit Comprising a Resistor and Capacitor - Assignment Example

 Assessment Details: Assessment 2.1 You are required to produce a report detailing how you would construct and test an electronic circuit. This does not involve you actually carrying out the laboratory experiment yourself. (1) You need to detail a circuit comprising a resistor (R) of 1 kilohm (1KΩ) and a capacitor (C) to produce: (i) a first-order low pass filter with a cut-off frequency of 2.5KHz The design below shows the operation of the first order filter circuit with a one resistor R of 1 kilo Ohms and a fixed capacitor C. It also has a power source V, switch S for regulating the cut off frequency and light emitter diode. The point where the experiment has the diode is in the no-signal condition. The value of the capacitor required to create the frequency of 2.5 KHz is calculated by multiplying the frequency by the resistance. Capacitor value = frequency * Resistance Capacitor value = (2500 * 1000) Coulombs Capacitor value = 2500000 Coulombs (ii) a first-order high pass filter with a cut-off frequency of 4KHz You are required to produce a circuit diagram for each case, and calculate the value of the capacitor required to meet the frequency response requirements stated. The design above shows the operation of the first order filter circuit with a one resistor R1, R2, R3 and R4 each of 1 kilo Ohms. It also shows fixed capacitor C, a power source V, switch S for regulating the cut off frequency and light emitter diode. Capacitor value = frequency * Resistance Capacitor value = (4000 * 4000) Coulombs Capacitor value = 16000000 Coulombs (2) You need to detail a laboratory experiment stating how you would test these two circuits. You need to include the following sections in your account: (i) Aim of the experiment – a brief introduction to the experiment This is an experiment to test the behaviour of the designed first order filter circuits. It uses various ranges of cut-off frequencies to determine the appropriate capacitor values that are required for the first order filter circuits. (ii) Construction of the circuit: How you would construct the circuit suitable for this experiment: this may involve (a) a prototype board (soldered or plug-in type) using discrete resistor and capacitor components, or (b) a resistor box (i.e. the type with adjustable dials to select the required value) and a similar capacitor box. a) The process of circuit design for the experiment involves identifying the required components of the circuit, with the required specification. The next step involved is by drafting a prototype which has the presentations of the discrete resistor, capacitor box, power source, switch and the diodes. b) In an alternative design, after identifying the right components for the experiment, the experiment drafts a prototype presenting signal generator (In this case, the light emitter diode, capacitor box and capacitor box for the purpose of varying the resistance in the entire circuit). (iii) Equipment used for the experiment. This may involve a signal generator, an oscilloscope, suitable connecting wires and any other suitable laboratory equipment you would need. Component Symbol Variable Resistor Variable Capacitor Signal Generator (Light Emitter Diode) Wire Power Source Switch Oscilloscope (iv) Method/Process including Diagrams: How you would conduct the experiment. State any specific measures you need to take to ensure the experiment is carried out correctly and to obtain accurate results. Produce diagrams as necessary to show the set up of the experiment. To conduct the experiment, the experiment first designs the prototype of the design as a draft. The design will be as shown in the diagram below: In the diagram, O represents Oscilloscope, D represents the light emitter diode (Signal regulator), C represent capacitor (Capacitor Box), R represent the variable resistor (Resistor Box), S represent the switch while V represent the power source. To get accurate design, the design will have to use the resistor box to vary the values of the resistance and the Capacitor Box to vary the capacitor values for different observations of the oscilloscope frequencies as suggested by Dailey (2001). For example, the design will set the resistance at 4Kilo Ohms, and then the measurements of frequency from the oscilloscope are taken. (v) Measurements: state all measurements you need to take to derive the filters’ characteristics from 20Hz to 10 kHz. Produce a table that you would need to fill in for the experiment, e.g. frequencies measured, signal levels, etc. The measurements that will be needed to reduce the filter frequency from 20 KHz to 10 KHz is set by gradually reducing the resistance value until the required frequency value is obtained. This process assumes that the capacitor value is constant such as Q = 2000 Coulombs. Calculation then makes use of the model F = Q / R for various values of R. R (kΩ) Frequency (KHz) Signal Level 100 20 5 110 18.18181818 6.05 120 16.66666667 7.2 130 15.38461538 8.45 140 14.28571429 9.8 150 13.33333333 11.25 160 12.5 12.8 170 11.76470588 14.45 180 11.11111111 16.2 190 10.52631579 18.05 200 10 20 (vi) Calculations: Since the frequency response is given as decibels (dB) you need to convert the signal input / output levels in to dBs. (note – Gain, dB = 20log Vout / Vin ) The frequencies are then converted into dB by the following model dB = 20 log (Vout)/ (Vin). Take Vout /Vin for the third column. Signal Level (Vout/Vin) dB 5 13.97940009 6.05 15.63510749 7.2 17.14664993 8.45 18.53713418 9.8 19.82452151 11.25 21.02305045 12.8 22.14419939 14.45 23.19735694 16.2 24.19030029 18.05 25.12954412 20 26.02059991 Graphs Frequency against Resistance Signal Level against Resistance (vii) Conclusions and Discussion: State any issues which need special attention. Discuss any conditions, or factors that may influence the accuracy of results that may be obtained. In the experiment, there is need to ensure that the capacitor value remains constant so that there will be consistent results. It also requires every variable factor to be reset before taking any further measurements for the filter frequencies. Finally, there has to be a standard form of rounding off values. For example, all the values can be rounded off to 2 decimal places or to three significant figures. This creates an even treatment to all the measures, and generates proportional relationship between the variables. Reference Dailey, D., 2001. Electronic Devices and Circuits, Discrete and Integrated. New Jersey: Prentice Hall. Read More