rf lab report 1

Swinburne University of TechnologyFaculty of Science, Engineering and Technology

EEE40008/EEE80004 RF Circuit DesignLab 1 – 1-port and 2-port passive networks

1. Student Name Thang Nguyen ID# 100050487

2. Student Name Aaron Watkins ID# 6161952

Aims1. To design and analyse some simple passive circuits.2. To be familiar with the various parameter sets for 2-port networks.3. To appreciate the parasitic effects in basic components at high frequencies.4. To gain experience in the use of a computer-aided design tool (National Instruments - Multisim) in the design

and analysis of electronic circuits.

Assessment

This laboratory has a weighting of 10 % of the total subject marks, and is over two laboratory sessions.

Preliminary (failure to do preliminary may result in exclusion from the lab) work is worth 35 % of this lab. Assessment is based on demonstration in the laboratory and correct completion of this lab sheet. The experiment is to be completed in pairs.

Note: All circuit diagrams and waveforms must be from the Multisim program – hand-drawn diagrams will not be accepted.

Introduction

Two-port networks can be described in terms of various parameter sets, such as the z, y, h, ABCD, and S parameter sets, where

z−parameters → ¿(v1 ¿)¿¿

¿

¿¿

Attenuators are used to adjust the levels of signals within different parts of a system while still maintaining the correct impedance. They provide a specified attenuation while ensuring that the input and output of the network remains Zo as long as the other port is also terminated in Zo. They offer isolation, and can be used to improve the match between circuits to ensure a low reflected power. A measure of match is called the return loss which is 10log|S11|2. Typically a return loss of more than 20 dB is required, which implies that the reverse power is less than 1/100th

of the incident power. Note that a 20 dB return loss is equivalent to a VSWR of 1.22.

Figures 1 and 2 show T and π implementations of attenuators. The attenuation is equal to |S21|2, which is also the transducer gain. Since the network is passive, S21 = S12. If the attenuator is placed in a transmission line with characteristic impedance Zo, then S11 = S22 = 0, and Zin = Zo.

Figure 1 – T-type attenuator Figure 2 – π-type attenuator

Required Software: National Instruments Circuit Design Suite

EEE40008/EEE80004 RF Circuit Design Lab. 1 – 1-port and 2-port passive networks 1 of 19

Preliminaries (35 % of this lab.)Workings for your preliminaries must be shown in the space provided.

A. The T-type attenuator of Figure 1 is placed in a transmission line with characteristic impedance Zo, which is terminated in a load impedance of Zo. Find the values of R1 and R2 if it is to provide an attenuation of 9 dB, with Zo = 50 Ω.

Figure 1 (repeated)

Workings:

R1 = Ω R2 = Ω


6 marks

B. For the generic T-network of Figure 3, find the impedance, admittance, and ABCD matrices, in terms of ZA (or YA), ZB (or YB), and ZC (or YC).

Figure 3

Workings:


[Z ] = ¿ [ ¿ ] [ ¿ ] [ ¿ ] [ ¿ ] [ ¿ ]¿¿

¿

[ABCD ] = ¿ [ ¿ ] [ ¿ ] [ ¿ ] [ ¿ ] [ ¿ ]¿¿

¿C. A 2-port network is formed from the cascade of two T-type attenuators (each of 9 db attenuation – use values

obtained in part A of preliminary).


8 marks

(i) Using the relationships of equation (4), derive the ABCD matrix for the above network.


(ii) Confirm that your results in part (i) are correct by using the fact that the overall ABCD matrix of two networks in cascade is the product of the ABCD matrices of the individual networks.


8 marks

D. A passive component is modelled by the circuit of Figure 4.


2 marks

L

CR

Figure 4 – model of a passive element.

(a) Derive the expression for the impedance Z in terms of R, L, C, and ω.

(b) If R = 1 kΩ, L = 1 nH, and C = 0.2 pF,

(i) Sketch the magnitude of Z against frequency ω.

(ii) What is the value of the resonant frequency fo?

E. Determine the input impedance Zin of the network shown in Figure 5 using basic circuit analysis. The frequency of operation is 2 GHz.


2 marks

2 marks

2 marks

Z

Figure 5

Zin =

OK _____________ (supervisor’s initials and grade, in %)

Part i:

Use Multisim to construct the 9 dB attenuator of Figure 1, with component values obtained in your preliminary.


5 marks

Insert a network analyser into your schematic, and connect P1 and P2 of the network analyser to the input and output ports of your network respectively. Default 50 Ω terminations are used by Multisim, at the input and output ports. Hence, it is not required to insert these resistors.

Double click on the network analyser. Click on the Simulation Set.. box, and choose appropriate values for the Measurement Setup for simulation at a fixed frequency of 200 MHz. Perform a simulation run by clicking on the

RUN icon, . From the Measurement mode, obtain values (in rectangular format) for the Z-, and Y-parameters, and complete Table 1.

Schematic of Figure 1 (from Multisim).

Z-parameters(simulated)

Z-parameters(calculated)

Y-parameters(simulated)

Y-parameters(calculated)

Z11 = 1.289 64.45 Y11 = 1.286 0.026Z12 =0.812 40.6 Y12 =-0.81 -0.0162Z21 =0.812 40.6 Y21 =-0.81 -0.0162Z22 =1.289 64.45 Y22 =1.286 0.026

Table 1: Z, and Y parameters for the network of Figure 1 at 200 MHz.

Do the values agree with your preliminary work?

Answer: The values simulated from Multisim are normalised by 50. Therefore, they are matched with the preliminary work, as it can be seen from the table 1.

Obtain the ABCD-parameters of the network using the preliminary work in part B.

[ABCD ]=[ Z11Z21 ∆ZZ21

1Z21

Z22Z21

]=[1.587 61.710.025 1.587 ]


14 marks

Part ii:

Connect an AC signal voltage source via a series resisor of 50 Ω to the input port of the attenuator of part i, and terminate port 2 with a 50 Ω resistor. Using AC analysis or otherwise, show that an attenuation of 9 dB is achieved.

Schematic of circuit to measure the attenuation of Figure 1 (from Multisim).

Simulation results:

Comment: As it can be seen from the simulation result, the attenuation:Attenuation = V(5)-V(1)= -9dB


Part iii:

Connect two 9 dB attenuators in cascade. Use Multisim to find the ABCD parameters of the two-port network

Schematic of circuit to find the ABCD parameters of the two-port network (from Multisim)

Measurement set-up for parameter A (from Multisim)

Simulated value of A:

A =v1v2

= 122.97

=4.04

The value calculated from preliminary: A = 4.04


Measurement set-up for parameter C (from Multisim)Simulated value of C:

C =i1v2

=0.2332.97

=0.0784

The value calculated from preliminary: C = 0.0781

Measurement set-up for parameter B (from Multisim)Simulated value of B:

B =v1−i2

= 120.0614

=195.44

The value calculated from preliminary: B = 194.08


Measurement set-up for parameter D (from Multisim)Simulated value of D:

D =i1

−i2= 0.2480.0614

=4.04

The value calculated from preliminary: D = 4.04

Do the simulated values agree with the theoretical values in part C of the preliminary?

Answer: As we can see from the above results, the simulated values are the same with the theoretical values of the preliminary.

Part iv:

Use Multisim to capture the circuit of Figure 4 (with R = 1 kΩ, L = 1 nH, and C = 0.2 pF) and insert a 1A AC current source across the input terminals.

Schematic of Figure 4 (from Multisim).


12 marks

Perform an AC analysis to obtain a plot of the input voltage against frequency.

Plot of input voltage against frequency (from Multisim)

From the frequency plot,

(a) The model of Figure 4 best represents which basic element: resistor, capacitor, and inductor?

Answer: As can be seen from the plot of input voltage against frequency, the impedance reduced against frequency. Therefore, the model of figure 4 best represent the capacitor and inductor.

(b) Justify the values (R, C, and L) of the model using the frequency response curve. You may need to ‘zoom in’ to get better accuracies.

Plot the value R of the model using the frequency response curve


Plot the value C of the model using the frequency response curve

Plot the value L of the model using the frequency response curve

(c) Is the value of the resonant frequency fo according to the value predicted in the preliminary?


Plot the resonant frequency fo

It can be seen that the value of the resonant frequency fo is matched with the value predicted in the preliminary.

Part v:

Use Multisim to capture the circuit of Figure 5, and through the appropriate simulation, verify that the preliminary work of part E is correct.

Schematic of circuit to measure the input impedance of Figure 5 (from Multisim).


15 marks

Simulation waveforms or plot to measure the input impedance of Figure 5 (from Multisim).

By adding a voltage input as following the above circuit, we can get the value of the input impedance:Zin = -102.2 - j4.543 Ω. This is matched the calculated value in the preliminary.

Part vi: Using the ZY- Smith Chart, find the input impedance of the network shown in Figure 5 at 2 GHz. Workings must be clearly shown on the Smith Chart.

Normalise the value of R, C, and L:

ZR=2550

=0.5

ZL1=ωL150

=0.5

ZL2=Z L3=ωL250

=1

ZC 1=ωC1150

=1.1

ZC 2=ωC2150

=1

- At A: YA = 2- At B: YB = 2+j


8 marks

- At C: YC = 0.5-j- At D: YD =0.5-2j- At E: YE = 0.5+1.9j- At F: YF = 0.5-0.1j

The input impedance of the network identified by using ZY Smith Chart:Zin = 1.92 + 0.38j

Multiply by 50: Zin = 96 + 19j Ω

Comment: The result is slightly different from the simulated value or calculated value.


12 marks

rf lab report 1

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