20331143 RF AND MICROWAVE COMPONENT AND SYSTEM DESIGN, JACOBS UNIVERSITY BREMEN PROF. DR. SOREN PEIK 1

Design Project RF Design 2016Alee Kazmi, Department of Electrical Engineering, Jacobs University Bremen

Abstract—The goal of this project was to design a LinearLow Noise(LNA) microwave amplifier circuit with maximumtransducer gain.

Keywords—Amplifiers, Stability, µ test, AWR NI Environment

I. INTRODUCTION AND THEORY

A. Matching NetworksBased on the voltage divided rule, the power consumed

by one of the two impedances is maximized when theirimpedances are equal. Network matching is the procedure ofdesigning the input impedance of an electrical load or theoutput impedance of its corresponding signal source to maxi-mize the power transfer or minimize the signal reflection. Anysingle-stage microwave transistor amplifier can be modeled bythe following circuit-:

Fig. 1: General Transistor Amplifier Circuit

B. StabilityStability, in referring to amplifiers, refers to an amplifier’s

immunity to causing spurious oscillations. The oscillations canbe full power, large-signal problems, or more subtle spectralproblems that one might not notice unless one carefullyexamines the output with a spectrum analyzer, one hertz ata time! Unwanted signals may be nowhere near the intendedfrequency but will wreak system havoc all the same. In anotherextreme, instability outside one’s band may drop the gain ofyour amplifier by 20 dB inside the band, which should betreated immediately. These types of problems are usually thetricky ones to solve. Either one can plot stability circles tocheck stability or use the more preferred, µ test.

C. Noise FigureNoise Figure is the measure of degradation of the signal

to noise (SNR) ratio, caused by the components in a radiofrequency signal chain. Its units are decibels and can beexpressed mathematically as-:

NF = 10 log 10

(SNRin

SNRout

)= SNRin,dB − SNRout,dB

II. STEPS TO BE TAKEN

First of all, the project will be made and simulated inthe NI AWR Project software. Then, the board will bephysically constructed using the exported .dxf file from theAWR software. Using a network analyzer, the gain acrossvarious frequencies shall be measured and compared withthe theoretical maximum gain and the graph from the AWRsoftware.

III. PARAMETERS

For my case, I was given the following parameters to use-:

Transistor BFP540Bias Point - Vce 2VBias Point - Ic 20mA

Center Frequency 2.50GhzBandwidth 100MHz

Transducer Gain 10dBNoise Figure 2.5dB

Stability Unconditionally StableInput Match S11 = -15 db

Output Match S22 = -15dB

IV. PROCEDURE

A. Calculating S valuesFirst of all, we needed the S values for my particular

amplifier model. To do that, I created a BFP540 amplifiermodel in AWR and entered my biasing values in it. Aftersimulating it, I viewed the reference doc and went over tomy biasing value at 2.5Ghz and retrieved the S values whichgenerated the S matrix as follows-:

S =

(−0.423286 + 0.159103i 0.052442 + 0.059484i2.795082 + 5.126543i −0.069888 − 0.143929i

)The determinant of this matrix is referred to as the ∆ which

for my case-:

∆ = 0.2108 − 0.3853i

B. Calculating Matching NetworkNow we need B1, B2, C1, C2 which are defined as-:

Inputting these values in MATLAB yields for me-:

20331143 RF AND MICROWAVE COMPONENT AND SYSTEM DESIGN, JACOBS UNIVERSITY BREMEN PROF. DR. SOREN PEIK 2

B1 = 0.9860, B2=0.6282, C1 = -0.4640 + 0.1018i, C2= 0.0807 - 0.2735i

Next we need to calculate the ΓS-:

and the ΓL-:

Inputting these into matlab yields two values for each butchoosing the smaller value gives us-:

ΓS = 0.7604λ, ΓL = 0.6395λ

Now we need to refer to the smith chart to get thematching network lengths. The procedure is as follows. Firstwe find the absolute value and the phase of ΓS and the ΓL.Next I mark the phase on the smith chart and measure thelength of the absolute value using the relative coefficientmarker. Now I plot these points on the smith chart. Next Ishift these points on the VSWR circle. Now I bring thesepoints down to the radial and subract from the originalphase and VSWR values to get the electrical lengths which Imultiply with 360 to get-:

C. Calculating GainNow we need to calculate the theoretical gain of the system

which is-:

When I input this into MATLAB, I get-:

GT = 16.3785

Now, I run the simulation in the AWR Environment. Todo so, I add a new graph and add the magnitude of every Sparameter into the graph against the frequency axis. After abit of fine tunings the axis values and parameters -:

My theoretical maximum gain is slightly below the maximumgain from the graph for whose reason I could not figure outbut I suppose it has got to do with different capacitancevalues.

D. Stability TestNow we have to check for stability by performing a µ test

as follows-:

Inputting the values in matlab yields the following-:

µ = 1.3071

This is greater then 1 which means the system isunconditionally stable and we do not need to plot stabilitycircles to test for stability.

We then performed a similar µ sweep test in the AWREnvironment.

20331143 RF AND MICROWAVE COMPONENT AND SYSTEM DESIGN, JACOBS UNIVERSITY BREMEN PROF. DR. SOREN PEIK 3

As we can see, the graph at the desired 2.5Ghz frequency hasa µ value higher then 1 which again proves that the system isunconditionally stable. It should be noted that this amplifier isnot stable for frequencies roughly under 2.25Ghz since the µvalue drops below 1 there.

E. Shifting to Microstrip DesignNow, as mentioned in the instructions, the RO4003 substrate

was used from the Rogers Library which has a height of32mil and thickness of 17µm.Next, we make use of theTXline tool to translate these value on the RF level instead ofideal lines. The width of the elements stays the same whileonly the length changes as we get those values from theTXline directly.

The next is the bias diagram-:

The Tuning and the TX-Line tool-:

(a) TX-Line(b) Tuner

The Tuning tool was initally used to tune the value of theresistor to just put the stability circle completely outside thesmith chart. After tuning it looked like this-:

I got an R value of 175ohm as shown in the previoustuner screenshot. It should be noted that I also used the tuningtool to closely match the maximum gain of the microstripcircuit to that of the ideal circuit while making as minimalisticchanges as possible. The following were the S parametergraph obtained when I plotted for the full fledge RF circuit-:

I tried my best but was no where able to cross the value of13.71dB. Now I plot the µ stability graphs again. It can beseen that the system is stable as both µ values are above 1.

A Noise performance, i.e. Noise figure over frequency usingMWO was also plotted for the new LNA circuit and is asfollows-:

20331143 RF AND MICROWAVE COMPONENT AND SYSTEM DESIGN, JACOBS UNIVERSITY BREMEN PROF. DR. SOREN PEIK 4

F. Microstrip Physical DesignThe microstrip was finally compiled in AWR environment

and exported out using the .dxf format. Some minor changerwere later done by the professor to the diagram to accom-modate physical space. Unfortunately, I dont have the newschemetics with me and will be using my old submitted ones.The diagram and physical figures are as follows. As one cansee they do not match for the aforementioned reason.

(a) The physical design thatwas made. (b) The .dxf design

Fig. 3: Designs

G. Importing the graph from the Network AnalyzerThe experiment was performed and the graph from the net-

work analyzer was imported into AWR. It looked as follows-:

As it can be seen, the theoretical maximum gain at 2.5 Ghzis shown as 14.2dB which is quite close to what we got fromthe AWR simulation. Moreover, plotting the stability µ plotyields-:

The µ stability graph shows a value of 4.579 dB at 2.5Ghzwhich is greater then 1 and shows that it is stable at thatparticular center frequency.

V. CONCLUSION

The simulation that was made was quite close to the actualphysical parameters of the low noise amplifier. There wereslight variations of course but those were due to small factorsthat we assumed to be ideal in the simulation. One of thosefactors were the amount of solder used in soldering especiallywhen attaching the ports. We were also not required to plotthe stability circles because the µ test told us the result.

REFERENCES

[1] S. Peik, RF and Microwave Component and System design, Lecture Notes2016

[2] D. Pozar, Microwave Engineering, 3rd edition 2015[3] C. Bowick,Newnes, RF Circuit Design, 2nd edition 1997[4] A. Matsuzawa RF circuit design: Basics, 1st edition