A Two Port Network Biology Essay

A Two Port mesh topology Biology EssayAtwo- porthole neta kind offour-terminal networkor quadripole is anelectrical networkcircuit or device with two pairsof terminals to connect to external circuits. Two terminals embed aportif the currents applied to them satisfy the indispensable requirement known as theport condition theelectric current entering one terminal must equal the current emerging from the other. The ports constitute interfaces where the network connects to other networks, the points where shows atomic number 18 applied or outputs be taken. In a two-port network, often port 1 is considered the stimulus port and port 2 is considered the output port.The two-port network model is used in mathematicalcircuit analysis techniques to isolate portions of larger circuits. A two-port network is regarded as a colour box with its properties specified by a matrixof numbers. This allows the response of the network to signals applied to the ports to be calculated easily, witho ut solving for all the internal electromotive forces and currents in the network. It besides allows similar circuits or devices to be comp bed easily. For example, transistors are often regarded as two-ports, characterized by their h-parameters (see at a lower place) which are listed by the manufacturer. Anylinear circuitwith four terminals cigarette be regarded as a two-port network provided that it does not contain an independent source and satisfies the port conditions.Examples of circuits analysed as two-ports arefilters,matching networks, transmission lines, transformers, andsmall-signal modelsfor transistors (such as thehybrid-pi model). The analysis of inactive two-port networks is an outgrowth ofreciprocity theoremsfirst derived by Lorentz. In two-port mathematical models, the network is described by a 2 by 2 satisfying matrix ofcomplex numbers. The common models that are used are referred to asz-parameters,y-parameters,h-parameters,g-parameters, andABCD-parameters, ea ch described individually below. These are all limited to linear networks since an underlying confidence of their derivation is that any given circuit condition is a linear super role of various wretched-circuit and open circuit conditions. They are usually evince in matrix notation, and they establish relations between the variables (Two-Port Networks. (n.d.). InWikipedia. Retrieved October 25, 20012, from http//en.wikipedia.org/wiki/Two-port_network)The experiment is divided into two parts Part 1 is focused on gear up two-port network parameters (admittance and transmission parameters only). The process of measurement and calculations pass on be briefly illustrated in Theoretical Supplement part. We are aiming to investigate the relationships between the individual parameters and the parameters of two-port networks in cascade and parallel. Part 2 is focused on finding out the transient responses in two-port networks containing capacitive and inductive reactances.Theoretical SupplementsMeasurement of Admittance (Y-) ParametersThe equations to determine the parameters areI1 = y11V1 + y12V2I2 = y21V1 + y22V2i.e. I = Y.VY =y11 y12y21 y22whereare the Y parameters of the two-port network. Experimentally these parameters can be determined by short circuiting the ports, one at a time. Hence these parameters are overly termed as short-circuit admittance parameters.The following diagrams show the method to calculate the parametersWhen output port is shorted (as shown in configuration 2 below)V2 = 0.1Figure 2y11 = I1 / V1y21 = I2 / V1When foreplay port is shorted (as shown in Figure 3 below)V1 = 02Figure3y12 = I1 / V2y22 = I2 / V2Measurement of Transmission ParametersThe equations to determine the parameters areV1 = AV2 BI2I1 = CV2 DI2Or3Where t is the transmission parameters of the two-port network.Experimentally, the t-parameters can be obtained by short circuiting and open circuiting the output one at a time.The following procedure shows how to calculate the parameters siding port is open-circuitedi.e. I2 = 04Figure4A = V1 / V2C = I1 / V2Output port is short-circuitedi.e. V2 = 01Figure5B = V1 / I2D = I1 / I2Cascade Interconnection of two 2-port NetworksConsidering the 2 networks A and B which are connected in cascade, as shown in Figure 6 below. From this the transmission parameters of the combined cascaded network (N) is obtained. The method is demonstrated below.5Figure 6tN = tA.tB7Hence, the following result is obtained.8Parallel Interconnection of two 2-Port NetworksConsidering the two networks A and B which connected in parallel, as shown in Figure 7 below. The overall y-parameters of the combined network N can be obtained as follows6Figure 7I1 = I1A + I1BI2 = I2A + I2BV1 = V1A = V1BV2 = V2A = V2BAndHDropboxCamera Uploads2012-10-25 05.41.34.jpgIt can be seen that the overall Y-parameters can be obtained by summing the similar Y-parameters of individual networks A and B, when the A and B networks are not altered by the parall el connection.Transient Responses of Two-Port NetworksDamping Ratio is defined as the ratio of the existing resistance in damped harmonic motion to that necessary to produce critical damping. It is also known as relative damping ratio. We divide the transient responses into three types on the basis of damping ratio ,Over damped response ( 1),Under damped response ( Critically damped response ( = 1).The various conditions stated supra are described in situation below.Over damped Response In this case the roots of the characteristic equation are real and distinct. The solution to the input signal is a decaying exponential manoeuver with no oscillations and the transient response go forth be over damped. The response to the input signal is slow and has no overshoots or undershoots.Under damped The roots are complex in this case. The transient response will be under damped when Critically damped When = 1, the roots are real and equal, and the transient response to the input signal will be critically damped. There will be no oscillations whatsoever. This case is a desirable outcome in many industries.In this experiment, we are mainly using the second type, which is the under damped response.And the characteristic equation is given byS2 + 2nS + n2wheren = undamped natural oftenness = 1/( LC )n (1 2 ) = damped natural oftennessA484D667-ABED-4193-B38C-40120C378004 = damping ratio =Further critical details have been illustrated in the Appendix B of Laboratory manual of Experiment L212.ObjectivesTo measure the admittance-parameters and transmission parameters of two-port networkTo investigate the relationships between individual network parameters and two-port networks in cascade and parallel connectionsTo study the transient response of a two-port network containing capacitive and inductive reactances.EquipmentDigital Storage OscilloscopeFunction Generator (50)Digital MultimeterInductor with 2 inductance stepsCapacitors 22F, one CFResistors 33, 100 (2 number s), 220, 330, 560, 680, 3.9k, 4.7k (2 numbers), 5.6k, 6.8kBread-boardProcedureMeasurement of Admittance-Parameters and Transmission Parameters and to investigate the relationships between individual network parameters and two port networks in cascade and parallel connectionsSetup A touch the resistive network A as shown in Figure 8 below.With the network connected in the circuit, apply a sinusoidal voltage of 1 kHz, and amplitude 10 volts from jacket to peak atPort 1 with port 2 open-circuitedPort 1 with port 2 short-circuitedPort 2 with port 1 short-circuitedIn each case measure the voltage and current at the input and output terminalsThe input voltage is measured by observing the peak to peak foster on the scope of the oscilloscope while the output voltage is measured with the digital meter.Tabulate the results in turn off 1. (all the values measured should be in rms)Figure 8 The resistive network ADA60CACE-9B44-4522-A111-F57AC9F95897Setup BConnect the resistive network as show n in the Figure 9 below.With the network connected in the circuit, apply an identical sinusoidal voltage as in Setup A atPort 1 with port 2 open-circuitedPort 1 with port 2 short-circuitedPort 2 with port 1 short-circuitedMeasure the identical variant as in Setup A in the kindred way.Tabulate the results in the same shelve 1.0536D217-3D48-4F28-B37B-77F1CB823EEAFigure 9 The Resistive Network BCascaded SetupConnect the networks A and B in cascade as shown in the Figure 10 below.Measure the identical parameters with the identical voltage and applying the voltage at the same positions as was done in the previous two setups A B.Tabulate the readings in tabular array 1 again.32E83E0D-6633-4D97-A59B-4374AF22F541Figure 10 The Cascaded Network of Networks A BParallel SetupReconnect the individual networks A B in parallel as shown in Figure 12 below.Repeat the same procedures above with the same voltage as above to this network.Tabulate the readings in Table 1.591F8FFC-7083-4E49-88AD-9 6E019FAD63CFigure 12 The Parallel Network of Networks A BTable 1 (All values in rms)ResultsI2 = 0V2 = 0V1 = 0I1 (mA)V1 (V)V2 (V)I1 (mA)I2 (mA)V1 (V)I1 (mA)I2 (mA)V2 (V)Network A(measured)2.383.452.525.093.823.454.005.653.46Network B(measured)0.723.493.223.272.823.452.893.183.45Cascaded(measured)2.663.472.073.421.313.44Parallel(measured)13.2811.593.4610.3412.553.46QuestionsThe voltages V1 and V2 should not be connected to shift 1 and 2 of the scope simultaneously. Why?It can be ascertained from the circuit that both the ports V1 and V2 have different grounds. If V1 and V2 are connected simultaneously to send 1 and 2 of oscilloscope respectively, then the ground terminals of V1 and V2 will be short-circuited as they are connected through the oscilloscope. This would change the circuits configuration and would give us the readings for a completely different circuit which would differ a great deal from the accurate values.What should you do to the readings of peak to peak voltage in assure to make them compatible with the currents measured by the digital meter?The relationship between peak to peak values and its respective rms values ispeak to peak voltage = 2 x 2 x rms voltageThe current measured by the digital meter is in root-mean- unbowed value (rms). So it is needed to convert the peak to peak voltages to its rms value in order to be compatible with the currents measured by the digital meter. Hence the peak to peak value is divided by 2 x 2 to so that it is compatible with the currents measured by the digital meter.Compare the suppositional results with the measurement readings recorded in Table 1 for the interconnected two-port networks. Explain any of the diversitys in the two sets of results.Two kinds of parameters values are calculated and shown in Table 2 and Table 3. With this parameter values we can compare the difference in values of the measurement and suppositional readings.The parameter values in Table 2 shown below are defined asWhen the o utput-port is open, I2 = 0ThenA = V1 /V2C = I1/V2When the output port is shorted, V2 = 0HenceB = V1/I2D = I1/I2And Cascade (theoretical) is obtained by tN = tA . tBTransmission parametersABCDNetwork A(measured)1.36677.800.000941.33Network B(measured)1.081223.400.000221.16Cascade(theoretical) (Network A*Network B)1.622450.070.00132.69Cascade(measured)1.682625.950.001292.61 dowery difference between cascade (measured) and (theoretical)3.70%6.69%0.78%3.07%Table 2As it can be seen from the Table 2 above that there are slight differences between the theoretical and observational results of the transmission parameters of the individual network and the interconnected two-port networks. The difference is observed repayable to the experimental human errors, tolerance levels of electric resistances in networks and slight deviation due to the slight inaccuracy of equipment.The parameter values in Table 3 shown below are defined asWhen the output port is shorted, V2 = 0. Theny11 = I1 /V1y21 = I2/V1When the input port is shorted, V1= 0. Theny12 = I1/V2y22 = I2/V2And Parallel (theoretical) is obtained by Network A values + Network B valuesTable 3 Admittance ParametersAdmittance parametersy11y12y21y22Network A(measured)0.001480.001560.001070.00163Network B(measured)0.000950.000840.000820.00092Parallel (theoretical)(Network A+Network B)0.002430.002400.001890.00255Parallel(measured)0.003840.002990.003350.00363Percentage difference between Parallel(measured) and Parallel (theoretical)36.72%19.73%43.58%29.75%From Table 3, it can be observed that the difference between experimental and theoretical admittance parameters are quite large. The large difference is due to the same experimental errors and small tolerance of resistors or the existing voltage drop of the multimeter.Measurement of Transient Response of Two-Port NetworksECB52EDE-2A5E-423C-AE62-ECF870EBA09CFigure 13Connect the circuit as shown in the Figure 13 above with C = 22 FUsing a storage scope and with the inductor setting at position 1, inject 10V peak to peak square wave at V1. Choose frequency f of the input voltage such that the square waves leading edge simulate a step input with the transient response completed before the next voltage change. The frequency f is chosen to be about 4 Hz.Record the output wave shape V2 with the storage oscilloscope. Sketch the wave shapes and when the waveforms have been captured, use the oscilloscope cursor to measure the oscillation period T and the voltages Va and Vb as shown in the Figure 14 below.The waveform is shown in Figure i) below.71B3E9F8-C513-4F5A-9441-0C73C0A0C9B8V1 Input Voltage V2 Output VoltageTin Input signal period T Transient roundVa / Vb Transient Oscillation Voltage Ratio PeriodFigure 14Repeat the above procedure for the inductor setting at position 2. The waveform is shown as in Figure ii) below.Repeat the procedure for the two inductor settings with the capacitor changed to 100F. The waveforms are show as Figure iii) and iv) below respectively.Add a resistor R2 of 33 in series with inductor L as shown in Figure 15 below and select the inductor setting at position 1 with the capacitor = 100 F. The waveform is shown as in Figure v) below.Repeat all the procedures with R2 values of 100 and 220 . The waveform with R2 as 100 is shown in Figure vi) below.All measurements are recorded in Table 4 below.HDropboxCamera Uploads2012-10-25 06.12.32.jpgFigure 15Figure aFigure bFigure cFigure dFigure eFigure fFigure gConditionC=22FL = 1HC=22FL = 200mHC=100FL = 1HC=100FL = 200mHC=100FL = 1H and adjoin R2=33C=100FL = 1H and add R2=100C=100FL = 1H and add R2=220T(ms)48.019.038.594.580.20Period = 253.0t1 =130.0t2 =46.00V2 =2.531Va(v)3.001.460.7911.801.6871.250Vb(v)0.6330.7000.4080.5160.37500.5000Table 4Waveform FiguresLAAADS0001.BMPFigure i)LAAADS0003.BMPFigure ii)LAAADS0006.BMPFigure iii)Figure iv)LAAADS0007.BMPLAAADS0008.BMPFigure v)Figure vi)LAAADS0009.BMPQuestionsWhy are square waves at a higher frequency not use d as input?Square waves at higher frequencies are not used as input because frequency is related to time period by the relationship f = 1/T. So as the frequency is increased, the time period will become shorter and shorter. So it will take shorter time for the output power levels to stabilize after the input circuit stops drawing power. Hence the waveform obtained from the oscilloscope will not be clear enough for proper distinction.What causes the step input voltage to become an hesitate output voltage?The oscillating output voltage is caused due to the presence of the two reactive elements in the circuit, the inductor and the capacitor. The effect of charging and discharging of the capacitor and inductor causes the output to become an oscillating voltage.What are the effects of increasing the values of L and C?The undamped natural frequency n equals to 1/( LC ). If the values of L and C are increased, the undamped natural frequency will reduce simultaneously. Hence the oscillatio ns will become more damped. Thus the number of output oscillations will reduce.Calculate the theoretical frequencies of oscillation and compare with the experimental results.The theoretical frequency is given by the relation ft = 1/ (2 (LC)) Hz and the oscillation frequency is given by the relation f = 1/T. Using this relation we can tabulate the values.Figure aFigure bFigure cFigure dT(ms)48.019.038.594.51/T(Hz)20.8352.6325.9710.58ft (Hz)33.9375.8735.5915.92Percentage difference38.60%30.63%27.03%33.54%The difference in the values is caused by the tolerance levels of the reactive elements used in the circuit i.e. the inductor and the capacitor.Consider the circuit shown in Figure 13. Obtain the expression for the damping ratio of the circuit.A484D667-ABED-4193-B38C-40120C378004Damping Ratio is given by the formula, =The natural undamped frequency is given by the relation n = 1/ (LC). SinceR2 = 0, R1 = 330 and R3 = 100 , filiation the damping ratio of the circuit as shown in Figu re 13, the result is = (L/C)/860.Obtain the condition for the underdamped response in Figure 13.From the derived result obtained above, = (L/C)/860. For an underdamped response, the damping ratio, , should be less than 1, thusly (L/C)/860 What is the effect of adding resistance R2 in the LC circuit?A484D667-ABED-4193-B38C-40120C378004According to the formula of damping ratio =When R2 is added, the total value of increases. Depending on the value of R2, 1, even if the number of undershoots and overshoots is reduced, the response will be slower.ConclusionThe parameters of the two-port network, especially the Y-parameters and Transmission parameters (A, B, C, D) were determined experimentally. They can also be calculated theoretically. This experiment is aimed at comparing the differences between the experimental and theoretical values. The relationship between individual network parameters and two-port networks in cascade and parallel connections were also investigated. The resul ts obtained for these were shown in the calculations in the Questions answered previously. Hence if every individual parameter of the networks can be determined, the parameter of the combined system can be determined.Part 2 was focused on studying the transient responses of the experiment. The responses to the change of values in the RLC circuit in the two-port networks were recorded. By varying the values of the capacitor, resistor and inductor, it was observed that increase in the capacitor and inductor values decrease the oscillating frequency and also reduce the number of undershoots and overshoots in the response signal. By adding a resistor in series with the inductor, it was observed that the resistor increases the damping ratio of the circuit only the effect is still dependent on the final damping ratio of the circuit, .To summarize the conclusion, all the objectives as stated earlier were met in course of the experiment and a lot of important observations came to light in the area of two-port networks.