Microwave Wireless Communication System

Technical report, IDE0628, January 2006

Microwave Wireless Communication System

Master’s Thesis in Electrical Engineering Carl Dagne, Johan Bengtsson, Ingemar Lindgren

School of Information Science, Computer and Electrical Engineering

Halmstad University

Microwave Wireless Communication System

Master’s thesis in Electrical Engineering

School of Information Science, Computer and Electrical Engineering Halmstad University

Box 823, S-301 18 Halmstad, Sweden

January 2006

Description of cover page picture:

A microwave antenna for the 2.4 - 2.5 GHz band.

Preface

This project was performed during the autumn 2005 with Emil Nilsson and Arne Sikö as supervisors. We would like to sincerely thank both supervisors for their help with both theoretical and practical matters. Their knowledge and interest in the area has been a big aid to us in completing our work. We would also like to thank our opponent Ola Johnsson at FMTS, for his thoughts and comments.

Carl Dagne, Johan Bengtsson & Ingemar Lindgren Halmstad University, January 2006

i

ii

Abstract

The purpose of the project was to develop the hardware to a microwave wireless system working at the frequency 2.45 GHz. The functionality of the system should also be easy to understand since the system is to be used in an educational purpose. Much time has been spent impedance matching components, a task that proved to be harder than we expected. Other work that has been is layout of all parts, filter construction and the writing of an easy to understand thesis. After the parts had been completed, they were tested in a network analyzer and/or spectrum analyzer.

Successful full system test has been done up to 400 meters, the length the system is to be used for.

iii

Contents

PREFACE...I ABSTRACT ...III CONTENTS...IV

1 INTRODUCTION ... 1

1.1 BACKGROUND... 1

1.2 ASSIGNMENT... 1

1.3 M^ETHOD... 1

1.3.1 Prestudy... 1

1.3.2 Design and Simulation ... 1

1.3.3 Measurements and Tests ... 1

1.4 R^EADING INSTRUCTIONS... 2

2 THEORETICAL BACKGROUND ... 3

2.1 MICROSTRIPS... 3

2.2 IMPEDANCE MATCHING... 4

2.2.1 The Smith Chart ... 4

2.2.2 Scattering Parameters... 5

2.2.3 Impedance Matching with Lumped Elements (L-networks) ... 6

2.2.4 Impedance Matching with Microstrips... 9

2.3 F^ILTERS... 11

2.3.1 Bandpass IF Filter ... 11

2.3.2 Microstrip Filters ... 12

2.3.3 Lowpass Microstrip Filter... 15

2.3.4 Bandpass Microstrip Filter ... 17

2.4 MODULATION TECHNIQUE... 18

2.4.1 Phase Modulation ... 19

2.4.2 Modulator... 22

2.4.3 De-Modulator... 22

2.4.4 Phase Locked Loop ... 23

2.5 OSCILLATORS... 26

2.6 LOW-NOISE AMPLIFIERS (LNAS) ... 27

2.6.1 Impedance Matching of RF LNA ... 29

2.6.2 The IF LNA... 34

2.7 MIXERS... 34

2.7.1 Diodes ... 34

2.7.2 Single-Ended Mixers ... 35

2.7.3 Balanced Mixers... 36

2.7.4 Double Balanced Mixers ... 36

2.7.5 Impedance Matching of Downconverter ... 36

2.7.6 Impedance Matching of Upconverter ... 41

2.8 ANTENNAS... 42

2.9 CIRCULATORS... 43

2.10 POWER AMPLIFIER... 44

3 RESULTS ... 45

3.1 MIXERS... 45

3.1.1 Downconverter ... 45

3.1.2 Upconverter... 46

iv

3.2 FILTERS... 46

3.2.1 Lowpass IF Filter ... 46

3.2.2 Lowpass Microstrip Filter... 47

3.2.3 Bandpass Microstrip Filter ... 49

3.3 LOW-NOISE AMPLIFIER... 51

3.3.1 Microwave Low-Noise Amplifier... 51

3.3.2 IF Low-Noise Amplifier... 52

3.4 POWER AMPLIFIER... 53

3.5 OSCILLATOR... 54

3.6 MODULATOR... 54

3.7 D^EMODULATOR... 55

3.8 SYSTEM TESTS... 55

3.8.1 Receiver... 55

3.8.2 Transmitter ... 55

3.8.3 Transmitter Receiver Test ... 56

4 CONCLUSIONS ... 58

5 REFERENCES ... 59

6 PERMISSION... 62

v

1 Introduction

1.1 Background

Today wireless technology is used in many applications well integrated into our everyday life.

One of the challenges for designing a microwave system is that the functionality of the electronic components changes when dealing with the upper frequencies of the UHF band. This means for example the filter design will differ much from conventional design methods, and transmission lines have to be short to make sure they do not work as antennas and thereby disturb the system.

1.2 Assignment

The main purpose of this thesis is to construct a microwave link between Halmstad University and the Agellis laboratory. The system has to be fast enough to support a video link, which means a bandwidth of at least 4 MHz. The microwave link constructed will send signals at 2.45 GHz.

This frequency was used since it belongs to the 2.4 GHz to 2.5 GHz band, which is one of the ISM frequency bands and is free to use. This thesis focuses on the RF part while the software interface used to run the complete system will be designed by another thesis group. The complete system will also be used in laboratory exercises in a microwave communication course at Halmstad University. The difference between this project and other similar available products is that this project will not try to make a compact system solution, but a system where all components are visible and the functionality is easy to understand.

1.3 Method

The main goal of this thesis can be divided into the following three sub-goals: prestudy, design and simulation and measurements and test.

1.3.1 Prestudy

An exhaustive study on existing material about microwave systems and the parts included in such a system was the first thing done. The studied material consisted of books, articles and web sites.

1.3.2 Design and Simulation

After the prestudy, circuits were designed and simulated using PSpice and Orcad, produced by Cadence, and ADS 2004A, by Agilent.

1.3.3 Measurements and Tests

Laboratory measurements and testing of the designed circuits were done continuously during the project using spectrum analyzer, signal generator and network analyzer to control the simulated results. Finally, a test of the whole system was carried out.

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1.4 Reading Instructions

This thesis is intended to be read by persons studying, or with degree in, Electrical or Computer

Engineering. Basic knowledge of radio communication systems and filters is needed.

2 Theoretical Background

A wireless communication system consists of several parts. Below is a block scheme of a transceiver. This chapter will explain the functionality of the parts in such a system and some basic theory needed for understanding these parts.

Figure 2-1 Components of a transceiver system.

2.1 Microstrips

Microstrips are one type of transmission lines which are devices “used to transfer energy from one point to another efficiently” [4]. There are a number of different transmission lines, but the most important type for this project is microstrips. The microstrip consists of a ground plane and a strip conductor, separated by a dielectric substrate, as seen in figure 2-2.

Figure 2-2 Microstrip transmission line [3].

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Microstrips are used at microwave frequencies where they are more efficient than conventional wiring. A major advantage when using microstrips is that it is easy to connect surface mounted components. As with all other wires conducting a current, the microstrip also has an electric field, which travels from the strip conductor to the ground plane. But since the electric field is not strictly confined to the area under the strip conductor, the field will also travel from the edge of the strip conductor to a place on the ground plane that is not situated directly under the conductor.

This phenomenon is called fringing effect which will make the conductor seem electrically longer than it really is. This means that if a microstrip at quarter wavelength is wanted, the conductor has to be slightly shorter because of the fringing effects. Another thing that affects the length is the dielectric substrate that has a relative dielectric constant. But since the strip conductor has a dielectric substrate on one side and air on the other, an effective dielectric constant has to be calculated to compensate for the difference. A higher effective dielectric constant will then make the microstrip shorter because the speed of light is slower in a dens material, which in turn will make the wavelength shorter since λ=c/f.

This project makes use of coaxial cables that have a conductor in the middle and a ground plane around the conductor with a dielectric substrate in-between. Like the microstrip, the electric field for the coaxial cable will travel from conductor to ground. When a coaxial cable and a microstrip transfer signals from one to the other, the electric field has to change form and it is therefore important to add an extra microstrip to make this change possible. This extra microstrip should also have the characteristic impedance which in this case is 50Ω, a number that can be altered by changing the width of the strip conductor. The relation is that the smaller the impedance, the larger the width [4], [2].

2.2 Impedance Matching

The reason for doing impedance matching is to deliver maximum power to a load. The only requirement for a matching network to be found is that the load impedance, Z

L

, has a real part.

When dealing with impedance matching, there are two different categories usually mentioned.

The first one is matching of transmission lines, where it comes down to terminating the line with Z

0

, which is the characteristic impedance of the line. The other is matching a source or a load by deriving its complex conjugate [3].

2.2.1 The Smith Chart

The impedance matching can be simplified by using a Smith chart which is an easy-to-use tool

that can give an approximate solution when deriving an impedance matching network. It is

represented by circles and lines as can be seen in figure 2-3.

Figure 2-3 The Smith chart

The real axis passes horizontally through the middle of the chart, while the bent lines from the right hand side of the chart to the outer circle stand for complex values. The complex lines above the real line are positive while the lines below are negative. The centre of the chart represents the real value 1. It is also possible to find admittance values by turning the impedance chart 180 degrees.

When using the Smith chart, the matching is made by moving from the complex conjugate of the impedance to the centre of the chart by adding reactive elements that do not consume active power.

2.2.2 Scattering Parameters

A type of parameter that often is used when talking about impedance matching of a system or device is the scattering parameter, also called S parameters. An S parameter can be calculated using the following equation.

S

ij

=V

i-

/V

j+

The above equation says that S

ij

can be determined by sending an incident wave of voltage V

j+

into port j and measure the reflected voltage amplitude and phase V

i-

, coming out of port i. If

considering a simple two-port device, S

11

will give a value of how well the input is matched and

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S

22

will tell us how well the output port is matched. For a perfect match S

11

and S

22

should be zero, meaning that nothing of the signal will be reflected.

2.2.3 Impedance Matching with Lumped Elements (L-networks)

The simplest way of impedance matching is by using the L section. This kind of network uses two reactive elements to match load impedance. There are two possible configurations as shown in figure 2-4 below.

Figure 2-4 Different configurations for L-section matching networks.

When deciding which network to use, the Smith chart is used. First, the normalized load impedance is derived, z

L

=Z

L

/Z

0

. If this number lies inside the 1±jx circle on the Smith chart, the network in figure 1a should be used and if it is outside the circle, the network in figure 1b should be used.

The reactive parts in the figure above may be either inductors or capacitors. If the frequency is below ca 1 GHz, lumped elements can be used in the implementation. When dealing with frequencies above 1 GHz, the lumped elements should be converted into microstrips. This because of parasitic capacitances and inductances that becomes larger with increasing frequency [3].

Another way to see which network configuration to use when calculating the values of the

components in the network is to find out which network works for which region. The allowed and

the forbidden regions for the different kind of network configurations are shown in figure 2-5,

where an impedance should be connected to the right of the networks. The determination of

values for the reactive components can easily be approximated using the Smith chart. There are,

however, some basic rules to be considered when dealing with the Smith chart in this way. A

shunt component always moves on the admittance chart while a series component moves on the

impedance chart. By themselves, an inductor always moves on the positive side of the smith chart

while capacitors move on the negative side [2].

Figure 2-5 Allowed and forbidden regions for different network configurations [17].

Example

Design an L section matching network to match the impedance Z=100-j50Ω, if Z

0

=50Ω at the frequency of 500 MHz.

Solution

After normalizing the impedance to z=2-j1Ω, it is plotted on the Smith chart of figure 2-6.

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Figure 2-6 Impedance an admittance chart with Z and its complex conjugate plotted.

To achieve a match, the complex conjugate, Z

^*

, of the impedance has to be known. It is easily

found by changing the sign on the complex part of the impedance. As seen in figure 3, there are

two possible network solutions to the problem. When using the network with the shunt inductor,

the way to the centre of the chart is found by following the black lines b and c. b stretches from

0.2 to 0.5 on the admittance chart, i.e. it is 0.3 long, while c can be read to be 1.2. The values of

the capacitor and the inductor can now be found.

05 . 2 53

0 =

= fb L_a Z

π nH

305 . 2 5

1

0

=

= fZ c C_a

π pF

When calculating the values of the two reactances with the other matching network where there is a shunt capacitor, the formulas will differ slightly.

39 . 2 ₀ =4

= fZ C_b x

π pF

1 . 2 19

0 =

= f L_b yZ

π nH

where x is the length of the line from Z

^*

to the circle with the real value 1, but on the opposite side of the real axis. This gives x the number of 0.69. y is the same length as c but is measured on the opposite side of the real axis of the chart.

The results of these calculations are shown in figure 2-7.

Figure 2-7 The two resulting matching networks.

The first two values should be applied to a and the second two values to b.

2.2.4 Impedance Matching with Microstrips

When dealing with frequencies above ca 1 GHz, the normal performance of capacitors and inductors no longer applies. These lumped elements have to be substituted by microstrips to make a matching network. The most basic form of matching network is using single-stub matching.

The aim of using single-stub matching is to make the length of the stub and the transmission line in such a way that a match is found for the admittance, Y. There are two ways of doing this when using a single-stub match. These are shown in figure 2-8.

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Figure 2-8 Single-stub matching network with a) open circuit stub and b) short-circuit stub.

The stub will act differently depending on the length of the line. The open circuit stub will be capacitive when its length is from 0 to λ/4 and inductive when from λ/4 to λ/2. The short-circuit stub will act in the opposite way compared to the open circuit stub. In microstrips, short-circuit stubs are difficult to realize which means that the open circuit stub often is used [18].

Example

Find the matching network for the admittance load, Y

L

=0.3+j0.3, using microstrips.

Figure 2-9 Smith chart for the matching network.

Starting at the load, the length of the microstrip is found by moving toward from point A to point B while keeping a constant distance from the centre of the chart. This distance is found to be 0.376 λ. The length of the open stub can then be found to be 0.152 λ by moving from point B to the centre of the chart and measuring the length of the stub on the outermost scale of the Smith chart.

2.3 Filters

Several filters are needed in a microwave system like the one in this project where their main purpose is to shape the signal spectrum. As can be seen in figure 2-1, various filters are needed.

These filters are bandpass IF filter and bandpass RF filter, but a RF lowpass filter will also be needed to filter out the harmonics from the local oscillator.

2.3.1 Bandpass IF Filter

The IF bandpass filter made with the Cauer technique, has a centre frequency of 70MHz and a bandwidth of 10MHz. The lower stopband extends from zero to 60 MHz and the other stopband reaches from 80 MHz to infinity.

6 2

6 1

6 2

6 1

10

* 80

* 2

10

* 60

* 2

10

* 75

* 2

10

* 65

* 2

π ω

π ω

π ω

π ω

=

=

=

=

S S C C

If multiplying the two passband frequencies and the two stopband frequencies and comparing these two products, it is easily seen that they differ from each other. One frequency then has to be changed to make them equal. The first stopband frequency is the chosen to be changed and will be given the new frequency 60.9375 MHz.

The next step is to use frequency transformations to convert to lowpass filter.

6 1

2

ω

2

π

*10*10

ω

− =

=

Ω_{C C C}

rad/s

6 1

2

ω

2

π

*19.0625*10

ω

− =

=

Ω_{S S S}

rad/s

The order of the filter can then be found to be N=4 using MatLab. For the network configuration, a π-network was chosen and the normalized values were found to be C

1

’=0.9307, C

2

’=0.2191, C

3

’=1.631, L

2

’=1.063, L

4

’=0.8307, R

1

’=1, R

2

’=1, where R

1

’ and R

2

’ are the normalized values to the 50Ω impedances.

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Figure 2-10 The normalized lowpass filter.

Frequency transformation was made to get the network of the bandpass filter. The values were calculated to be C

1

=296pF, C

2

=69.74pF, C

3

=6.14pF, C

4

=519pF, C

5

=7.86pF, L

1

=17.6nH, L

2

=74.5nH, L

3

=846nH, L

4

=10nH, L

5

=661nH, R

1

=50Ω, R

2

=50Ω.

Figure 2-11 The bandpass filter.

Since most of the values of the lumped elements are not available as standard components, the values had to be changed. The new values were found using ADS. C

1

=330pF, C

2

=82pF, C

3

=8.2pF, C

4

=470pF, C

5

=8.2pF, L

1

=15nH, L

2

=68nH, L

3

=680nH, L

4

=10nH, L

5

=680nH, R

1

=50Ω, R

2

=50Ω. Changing the values of these elements will of course change the characteristics of the filter. These changes will however be acceptable according to ADS. However, it is very important to test the filter in a network analyzer to confirm that it works. This is not certain since the components have 5% tolerance which means that the characteristic of the filter still can change.

2.3.2 Microstrip Filters

When dealing with frequencies above ca 1 GHz, it is better to use filters constructed with

microstrip transmission lines instead of lumped elements. There are lumped elements that can be

used for high frequencies but since these have standard values another advantage using

microstrips is that any length and width of the transmission line can be made. There are a number

of different configurations to use when designing microstrip filters. When it comes to bandpass

filters, two frequently used types are coupled line and capacitively coupled line filters [11].

Figure 2-12 shows these two types, where both types can have different lengths, width and spacing between the lines.

Figure 2-12 a) Capacitively coupled line filter and b) coupled line filter.

Open stub filters are another type of filter that are used in microwave systems, but are used to create lowpass filters.

Figure 2-13 A third order open stub filter with 50 ohm transmission lines.

Designing open stub filters is done with the use of Richard´s transformation and Kuroda´s identities. Richard´s transformation is used to convert from lumped elements to transmission line sections.

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Figure 2-14 Richard´s transformation for an inductor and a capacitor [3].

The length λ in 2-15 is for the centre wavelength ω

0

. Kuroda´s identities are used because it is

difficult to implement series stubs in microstrip filters. This is done by separating filter elements

by using transmission line sections [3].

Figure 2-15 The four Kuroda´s identities used to convert from open-circuited stubs to short-circuited stubs and vice versa, where n²=1+Z2/Z1 [3].

2.3.3 Lowpass Microstrip Filter

The reason to make a lowpass filter is mainly to eliminate the harmonics from the local oscillator (LO). Since the LO is oscillating at 2.38 GHz, the harmonics will be at N*2.38GHz, where N is an integer greater or equal to 2. Using MatLab, the lowpass was calculated to be a fifth order filter with the passband frequency f

c

=2.5 GHz. The normalized values for the filters can also be found using MatLab.

g

1

=1.7058

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16 g

2

=1.23 g

3

=2.5408 g

4

=1.23 g

5

=1.7058

A T-network was chosen for this filter. Richard´s transformation is used to transform the T- network from lumped elements to open- and short-circuited stubs, figure 2-16 a. Unit elements are added to make the use of Kuroda´s identities easy.

Figure 2-16 Transformation from short-circuited stubs to open stubs using Kuroda´s identities [3].

Denormalization with the characteristic impedance 50Ω and the frequency 2.5 GHz gives the impedances of the final filter. The width of the transmission lines were then calculated using TX- line.

After these calculations were done, the filter was implemented in ADS and the parameters were tuned to achieve best possible result.

2.3.4 Bandpass Microstrip Filter

Coupled line filter technique was used and the centre frequency should be f

0

=2.45 GHz, with a bandwidth from 2.4 GHz to 2.5 GHz.

Where

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k=N-1, Z

0e1

means the first even mode characteristic impedance and Z

0o1

means the first odd mode characteristic impedance.

Using the characteristic impedance Z

0

=50Ω gives the following impedances on the coupled lines.

Z

0e1

=62.09 Z

0o1

=37.91 Z

0e2

=49.93 Z

0o2

=44.38 Z

0e3

=49.93 Z

0o3

=44.38 Z

0e4

=62.09 Z

0o4

=37.91

The length, width and spacing between the lines can then be poorly estimated with TX-line and optimazation and/or tuning with ADS or some other computerized tool is a must to make this a working filter. The final filter can be found in figure 2-17.

Figure 2-17 The complete bandpass filter.

The filter is constructed of 4 regions, where the first and the fourth are the same, just as the second and the third are the same. The first and the last element are 50Ω impedances, the first and fourth region consists of 2 lines with width W

1

=27.5 mils, length L

1

=848 mils and the spacing S

1

=27 mils. The second and the third region are constructed with W

2

=39 mils, L

2

=838 mils and S

2

=75 mils. Mils is one thousandth of an inch and is a very common measure.

2.4 Modulation Technique

The function of the modulator and de-modulator is of course to modulate and demodulate the signal. There are three major ways to modulate a signal. The first way is amplitude modulation (AM). AM work in such a way that the information signal causes the carrier signal to increase and decrease in amplitude, where high amplitude corresponds to a 1 and low amplitude corresponds to a 0. This form of modulation is very sensitive to noise and is mostly used for sending data at a low bit rate.

The next way to modulate a signal is by frequency modulation (FM). The information signal makes the carrier signal to increase or decrease in frequency and two different frequencies correspond to 1 and 0.

The last way of modulating a signal is by phase modulation.

2.4.1 Phase Modulation

Phase modulation, or phase shift keying (PSK), is today one of the most used way of modulating data. There are also different ways of doing PSK, two examples are binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK).

BPSK uses different phase to represent binary 1 and 0.

The type of modulation used in this project is QPSK. QPSK uses four different phases to represent 00, 01, 10 and 11 and uses therefore the bandwidth more efficiently since every phase shift represents two bits instead of one bit, as in BPSK.

Figure 2-18 Phase diagram [1]

The modulation of the signal is done by dividing it into 2 signals, I and Q, multiplying the I with a sinusoidal signal at 70 MHz and multiplying the Q with a cosinusoidal signal at 70 MHz in a mixer. The results from the mixers are then added to each other to get the quadrature phase signal. In our case, the binary bits 0 and 1 will be represented by the logical levels -1 and +1. The theory of how to get the quadrature phase signal can be proven by the use of Euler’s relations.

j e t e

t j t j

) 2 sin(

ω

ω =

ω

⁻

⁻

) 2 cos(

t j t

j

e

t e

ω

ω =

ω

⁺

⁻

If I and Q equals 1, then

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) 4 / 2 sin(

) 2 2

2 ( 1

2 ) ( 1 2 )

( 1

2 ) 1 2 ( 1 2 )

1 2 ( 1

2 ) 2

cos(

) sin(

) 4 / ( ) 4 / (

4 / 4

/

π ω ω

ω

π ω π

ω

π ω

π ω

ω ω

ω ω

ω ω

ω ω

+

− =

=

=

−

=

− = + −

=

=

−

− +

=

+ =

− +

= +

+

− +

−

−

−

−

−

−

j t e e

e e

e j e

j e j

j e j

e j e j

e e j

e t e

t

t j t

j

j t j j

t j

t j t

j

t j t

j

t j t j t j t j

The result if doing similar calculations with the different kinds of input signal will be as shown in table 2-1.

Binary input I (after mixer) Q (after mixer) Sum

00 -sin(ωt) -cos(ωt) sin(ωt-135°) 01 -sin(ωt) cos(ωt) sin(ωt+135°) 10 sin(ωt) -cos(ωt) sin(ωt-45°) 11 sin(ωt) cos(ωt) sin(ωt+45°)

Table 2-1 Corresponding phase shift in the output signal for different binary input signals [1].

When the phase quadrature signal received on the other side of the system it has to be demodulated.

Figure 2-19 A simplified demodulator.

To make the demodulator demodulate the received signal correctly, it has to know when a signal

starts. It is therefore important to use a synchronizer circuit which in this case will contain a

phase locked loop (PLL), discussed later on, and an element that divides the frequency from the PLL by four. The basic function of the PLL is to multiply the IF signal frequency by four and by doing so eliminating the differences in phase shift as can be seen in the equations below [1]. One problem that could arise is that the local oscillator possibly could have a constant phase error because of the different path lengths between the signal going through the synchronizer and the one going through the divider.

) 4

sin(

) 4

* 4 / 3 4

* sin(

) (

) 4

sin(

) 4

* 4 / 3 4

* sin(

) (

) 4

sin(

) 4

* 4 / 4

* sin(

) (

) 4

sin(

) 4

* 4 / 4

* sin(

) (

π ω π

ω

π ω π

ω

π ω π

ω

π ω π

ω

+

=

−

=

+

= +

=

+

=

−

=

+

= +

=

t A

t A t s

t A

t A t s

t A

t A t s

t A

t A t s

After the signal has gone through the PLL, it is divided by four so that the original frequency is regained, without modulated phase shift. This means that the local oscillator in the demodulator is running at the correct frequency. The demodulation of the received signal is then be done by multiplying it in a mixer circuit. This can be mathematically proved by using Euler’s relations.

2 ) 2

cos(

2 ) cos(

2 ) cos(

2 ) 2

cos(

4 2

) 2

cos(

4

2 ) 2

sin(

) sin(

) 2 ( ) ( ) ( ) 2 (

) ( ) (

ϕ ω ϕ

ϕ ϕ

ω ϕ ω

ϕ ω ω

ϕ ϕ

ϕ ω ω

ϕ ω ϕ

ω ω ϕ

ω

ϕ ω ϕ

ω ω ω

− +

=

=

− +

= +

− =

− +

−

= +

− =

+

−

= −

− =

− ∗

= +

∗

−

+

−

− +

−

− +

+

− +

−

t t

e e t

e e

e e

j e e

j e t e

t

j j

t j t t j t

t j t

j

t j t

j t j t j

The only problem with this method is that it cannot distinguish between the phase shifts with a + or a – sign. Therefore, to decode all four quadrants, the input signal has to be multiplied by both a sinusoidal and a cosinusoidal waveform. The higher frequency also has to be filtered out, which is done by using a lowpass filter.

If multiplying the received signal with a cosinusoidal waveform at the same frequency, this will after a few steps give the following result [1].

2 ) sin(

2 ) 2

) sin(

sin(

)

cos(

ω

∗

ω

+

ϕ

=

ω

t+

ϕ

+

ϕ

t

t

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2.4.2 Modulator

The modulator, MAX2452, an integrated circuit (IC) was chosen from Maxim that filled the requirements needed for this project.

Figure 2-20 A block diagram of the modulator integrated circuit [7].

I and Q represent the two bits sent at every phase shift. These signals will have a frequency of 600 kHz. The I signal is then mixed with a sinusoidal signal and the Q with a cosinusoidal signal, both at 70 MHz, and added to each other to get the final quadrature phase signal. The local oscillator is run by a TANK-circuit that controls the operating frequency, which in our case will be oscillating at 140 MHz [1].

2.4.3 De-Modulator

The demodulator used is the MAX 2451 includes many of the parts that can be found in the

modulator.

Figure 2-21 Block diagram of the demodulator integrated circuit [26].

The input signal to the demodulator is the IF signal that is oscillating at 70.6 MHz. It is divided into two signals where one of these signals is mixed with a sinusoidal signal at 70 MHz and the other is mixed with a cosinusoidal signal at 70 MHz. The sinusoidal and the cosinusoidal signal are provided by the local oscillator. The difference between the modulator and the demodulator is that the frequency of the local oscillator in the demodulator is not decided by a TANK-circuit.

Instead, a phase locked loop (PLL) is used. By using a PLL the demodulator will be synchronized with the modulator sending the data [1].

2.4.4 Phase Locked Loop

Phase locked loops are analogue circuits that are commonly used in many analogue and digital systems. PLLs can be used for clock recovery in communication systems, frequency synthesizers in TVs and wireless communication systems to select different channels and much more. This is done by adjusting the PLL oscillating frequency to get it to match the desired frequency. PLLs are non-linear systems, but when in lock, their behaviour can be estimated with linear equations.

A PLL usually consists of a phase detector, a loop filter, a voltage controlled oscillator (VCO) and a frequency divider as shown in the figure below.

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24

Figure 2-22 Basic structure of a PLL [22].

The phase detector compares the input signal to the signal received from the voltage controlled oscillator (VCO). The bigger the phase difference, the bigger the output voltage from the phase detector. The loop filter makes the result from the phase detector smoother and passes it on to the VCO. The VCO then changes its oscillating frequency depending on the voltage at the input. If the PLL is stable and the system reaches a point where the two inputs to the phase detector are in phase, the signals will also have the same frequency since angular frequency is the derivative of the phase with respect to the time. When changing the number N in the frequency divider, the synthesizer output signal will change accordingly.

The phase detector can be built in different ways. One way is to use a double balanced mixer to multiply the input signals, but a much better way is to use a phase frequency detector (PFD). It contains two D flip-flops and an AND gate as shown in figure 2-23. If f

r

or f

v

goes high, the Up port or the Dwn port will go high respectively. When they both have the logic value 1, the AND gate will cause the flip-flops to reset. This means that the two output ports only are 1 the amount of time it takes the AND gate to reset the flip-flops. The waveforms for the ports to the PFD can be found in figure 2-24. When f

r

and f

v

are the same, the output ports Up and Dwn will also be the same. This means that when calculating Up-Dwn, the result should be zero for the two input signals to be equal. If for example f

r

oscillates at a higher frequency than f

v

, FF

1

will be set to one more often than FF

2

. The two flip-flops will however be reset to zero an equal number of times.

The result of this will be that the Up port will have a higher average value than the Dwn port.

Making the calculation Up-Dwn will then give a positive value which means that the VCO in the

PLL will be fed with a higher voltage, making it oscillate faster [22].

Figure 2-23 A PLL with two flip-flops and an and-gate [22].

Figure 2-24 Waveform of the PLL shown in the figure above [22].

The PLL used in this project has the disadvantage that it has no memory to remember for example the number in the frequency divider. The PLL therefore has to be reprogrammed every time the device is turned on. The reprogramming of the PLL will be done using a program called Codeloader 2 via a parallel cable.

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2.5 Oscillators

Oscillators are complicated nonlinear circuits to design. A simplified and linearized version of an oscillator can look like the one in figure 2-25. The two port oscillator consists of an amplifier and a linear filter H(s), as a feedback component.

Figure 2-25 Basic structure of an oscillator.

The input to the oscillator can be thermal noise or a step response that is removed once the oscillator reaches steady state but is necessary to start the device. Since the networks is supposed to oscillate, it has to have a pair of complex conjugate poles in right-half complex plane of the unit circle. The oscillator loop gain should be exactly one to prevent the circuit from attenuating or increase uncontrollably.

This project will be using a voltage controlled oscillator (VCO) MAX2753 to convert the signals to IF and RF. A VCO can be achieved by using a varactor in the filter and by doing this, the oscillation frequency is changed.

The output signal produced by the MAX2753 will be made to oscillate at 2.38 GHz. This means that there will be harmonics at n*2.38 GHz, where n is an integer.

Figure 2-26 Harmonics for the MAX2753 [27].

The harmonics of the oscillator can be seen in figure 2-26. The first harmonic is suppressed 30dBc (dBm compared to carrier) and the second harmonic 27dBc.

The inductor and the varactor of the tank circuit controlling the frequency are integrated on the circuit which simplifies making of the external circuitry.

2.6 Low-Noise Amplifiers (LNAs)

The smallest signal that can be received by a system defines the receiver sensitivity and is set by the noise. The largest signal that can be handled by the receiver without affecting the quality of the data, gives an upper power limit. The Low-noise amplifier (LNA) plays a very important role in the receiver design. Its main purpose is to amplify extremely low signals without decreasing the signal to noise ratio (SNR).

When designing a LNA there are many parameters to consider and it is impossible to design a LNA without trade offs. Some of the parameters that give a description of how well a LNA performs are gain, noise figure, stability, linearity, low power consumption and input and output match. Parameters that interfere with each other are for example low noise figure and good input match, stability and gain, IP3 and current consumption.

The first and most important step in a LNA design is the selection of transistor. There are three design parameters that first should be taken into consideration which are noise, gain, IP3 and decide what V

CE

and I

C

will give the best performance, information that can be found in the datasheet for the device.

LNA linearity is also an important parameter and a measure of it is the 3

^rd

order intercept point (IP3) which indicates how well the LNA performs in presence of strong nearby signals and how well it deals with harmonics. For bipolar junction transistors, the output-IP3 can be estimated using the following formula:

) 5

*

* log(

* 10

3 V

_CE

I

_C

OIP = [dBm] [25]

where V

CE

is in volts and I

C

is in mA.

The Input-IP3 can also be estimated taking the OIP3 subtracted by the gain.

After having chosen a suitable transistor, the next step is to choose DC bias circuitry. It should give stable thermal performance, be cost effective and simple solution that occupies smallest possible area. One of the simplest forms of DC biasing that fulfils the major requirements is shown in figure 2-27.

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28

Figure 2-27 Simple form of DC biasing [25].

This DC bias is good since a stable biasing point is wanted. If I

C

decreases, V

C

will increase which will result in a higher I

b

. Higher I

b

will in turn increase I

C

. If the temperature increases, I

C

will increase. This will lower V

C

causing I

B

to decrease which finally will cause I

C

to decrease.

For R

b

to have little influence on the source matching, which is important for the noise figure, the feedback network should be decoupled with an inductor. Another possibility bias feedback can be realized with an emitter resistor and a capacitor, shown in grey in figure 2-27. C

e

should present a short at the operating frequency to make its influence on gain and noise performance as small as possible.

Stability is the next thing to consider. The LNA should be unconditionally stable, which means that the device will not start to oscillate no matter what load is presented on the input or output port. Stability can be controlled using the s-parameters and by using them in the following equations.

21 12 22

11

S S S

S

S = −

∆

|

| 2

|

|

|

|

|

| 1

21 12

2 2

22 2 11

S S

S S

K − S − + ∆

=

If the intermediate value ∆S is less than 1 and the factor K (called Rollett Stability Factor K) is

larger than 1, the circuit will be unconditionally stable. There are some methods to make the LNA

stable. One of them is to use R-L-C feedback between collector and base in order to lower the

gain at lower frequencies and thereby improving the stability. Another method is to use a

matching filter, usually put at the output of the transistor to make the gain decrease for specific

narrow bandwidth at high frequency. Yet another method is to use an emitter feedback inductor in order to make the LNA more stable at higher frequencies.

The next thing to do is to match the noise and input return loss (IRL) of the source. A usual approach is to match the input impedance of the transistor with Γ

opt

which gives the best noise match. Normally, this means that the input return loss of the LNA will be sacrificed since the optimal IRL only can be achieved with a matching network that terminates the complex conjugate of S

11

. How this is done is shown in the calculation part of this chapter.

2.6.1 Impedance Matching of RF LNA

The low-noise amplifier used in this project will be the MAX2644 from Maxim. When calculating the matching network, there are several parameters that have to be known. These can be found in [20]. The scattering parameters are found to be

S

11

=0.5619/-35.54°

S

21

=5.6624/150.06°

S

12

=0.0236/68.36°

S

22

= 0.4043/5.00°

As can be seen in the scattering parameters, S

21

and S

12

differ a lot. This means that the device is active and is amplifying the signal travelling from port 1 to port 2. This also means that any matching circuitry placed at port two will affect the input reflection coefficient very little, compared to what a matching circuit at port 1 would affect the output reflection coefficient. In most passive devices, the two parameters, S

21

and S

12,

would be the same.

If looking at the suggested surrounding circuitry for the MAX2644 in figure 2-28 from the data sheet of the low-noise amplifier, it can be seen that there are already a shunt inductor and a series capacitor on the input, where the capacitor is to act as a DC block and the shunt inductor is a matching circuitry. This capacitor does not have to be taken into consideration when calculating the matching network since its value is very big (33pF) i.e. its reactance will be very small.

Figure 2-28 The surrounding circuitry of the MAX2644 low-noise amplifier [20].

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30

The first thing that will be checked is if the amplifier is unconditionally stable by calculating the intermediate value |∆S| and the stability coefficient K.

°

−

=

−

=

∆ S S

₁₁

S

₂₂

S

₁₂

S

₂₁

0 . 3021 / 6 . 1558

2901 .

| 2

| 2

|

|

|

|

|

| 1

21 12

2 2

22 2

11

− + ∆ =

= −

S S

S S

K S

Since the intermediate value is less than 1 and the stability coefficient is larger than 1, the amplifier is stable. It is now possible to calculate the maximum available gain.

42 . 17 ) 1 log(

| 10

|

| log |

10

²

12

21

+ − − =

= K K

S

MAG S dB

For a perfect match, S

11

should be 0, which means that nothing of the incident wave is returned to port 1. This is naturally done by a matching network. But, since the matching network should consider the noise figure the calculations will differ from conventional matching. Also, it is important to take the reflection coefficients into consideration since the matching network added to the input will make a difference to the reflection coefficient on the output and vice versa.

The next step is to calculate two intermediate quantities C

2

and B

2

so the load reflection coefficient can be found.

2 2 21 12 2

2

1

|

| 2

C K S S B

L

−

= ± Γ

Where

°

−

=

∆

−

= _{22 11}^* 0.25934/ 10.678

2 S S S

C

and

75646 . 0

|

|

|

|

|

|

1

₂₂ ² ₁₁ ^{2 2}

2

= + S − S − ∆ S =

B This gives

°

=

Γ

_L

. 39682 / 10 . 678

The next step is to find the source reflection coefficient by doing similar calculations.

1 2 21 12 1

2

1

|

| 2

C K S S B

S

−

= ±

Γ

Where

°

−

=

∆

−

= _{11 22}^* 0.46623/ 44.048

1 S S S

C

and

061 . 1

|

|

|

|

|

|

1

₁₁ ² ₂₂ ^{2 2}

1

= + S − S − ∆ S =

B This gives

°

=

Γ

_S

0 . 54733 / 44 . 048 Γ

in

and Γ

out

can now be calculated.

°

− Γ =

− + Γ

=

Γ 0 . 547 / 43 . 576

1

₂₂

21 12 11

L L

in

S

S S S

°

− Γ =

− + Γ

=

Γ 0 . 4019 / 9 . 9474

1

₁₁

21 12 22

S S

out

S

S S S

Since it is important to think about the noise, a noise figure circle is drawn to calculate the best match for the noise. According to the datasheet for the device the minimum noise figure of the transistor is F

min

=1.589 dB, the reflection coefficient for optimum noise figure is Γ

opt

=0.408/70.63°, the equivalent noise resistance of the transistor is R

N

=21.94Ω and the noise figure is 2 dB at maximum gain.

The first thing to do is to calculate the radius and the centre of the 2dB noise figure circle.

1172 . 0

| 63 . 70 408 . 0 1 50 | / 94 . 21

* 4

442 . 1 585 .

| 1 1

/ | 4

2 2

0

min

+ Γ = − + ∠ ° =

= −

_opt

N

Z

R F N F

°

∠ + =

= Γ 0 . 4558 70 . 63 1

C

_F

N

^opt

2988 . 1 0

)

|

| 1

(

²

+ = Γ

−

= +

N N N

R

_F ^opt

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Figure 2-29 Smith chart with noise figure circle and constant gain circle.

The next step would be to draw a gain circle around S

11*

and then match the point where the two circles intersects. However, this is not necessary since it can be seen that the complex conjugate to Γ

in

lies within the noise figure circle. It is therefore only necessary to match this complex conjugate. More about how to match with lowest possible noise can be found in [2].

Since this device will be working in the microwave region, it is better not to use lumped

elements. Instead, these elements will be substituted by microstrips. These will be derived from

the Smith chart.

Figure 2-30 The deriving of microstrip lengths using the Smith chart.

The match will be done as explained in the impedance matching chapter. Working backwards, the first thing that will be calculated is the length of the line on the input. The length will be found by moving from 1 toward the load to 2. This length is read to be .269λ and with a λ that according to TX-line will equal 84.4504mm at 2.45 GHz for the laminate chosen for this project, this means that the length of the line will be 22.72mm. The length of the open stub is then found to by moving from 3 to 0 which gives 0.146* λ=12.33mm. The length of the line and the stub for the output is found if doing the same way as with the input. The line will be .328* λ=27.70mm and the open stub .117* λ=9.88mm. ADS was used to tune these parameters and the final lengths (in mm) can be found in figure 2-31.

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Figure 2-31 The final matching network.

2.6.2 The IF LNA

A low-noise amplifier for the intermediate frequencies will also be needed in the system. The MAX2611 was chosen to meet the requirements. The s-parameters of the LNA are already very good, thus, no external matching are needed. According to the datasheet the LNA will amplify the input signal 19 dB with a noise figure of 3.6 dB.

2.7 Mixers

The purpose of using mixers is to convert a signal to a different frequency. To do this, a non- linear element is used that multiplies the two input signals. This element is most commonly a diode, but can also be a transistor. Mixers are three port circuits that have to be impedance matched at all ports to achieve good sensitivity and low noise. This can be complicated since several frequencies and their harmonics are involved. An important parameter for a mixer is its conversion loss, defined as

L

C

=10log (available RF input power/IF output power) dB [2].

Normally, the conversion loss is between 4 and 7 dB. A factor that affects the conversion loss of the mixer is the power level of the local oscillator signal. For minimum conversion loss, most LO powers should be more than 0 dBm and less than 10 dBm [2].

2.7.1 Diodes

A diode can basically be seen as a non-linear resistor. Its DC V-I characteristic can be expressed as

1)

−

=I_S(e ^V

I(V) ^α

where α=q/nkT, and q is the charge of an electron, k is Boltzmann’s constant, T is the temperature, n is the ideality factor and I

S

is the saturation current.

If the diode voltage is set to be

+ v

= V

₀

V

where V

0

is the DC bias voltage and v is an AC signal voltage. This will change the V-I characteristic for the diode and can by using Taylor series be expressed as

2 ...

) 1 (

0 0

2 2 2

0 + + +

=

V dV V

I v d dV

vdI I V I

where I

0

=I (V

0

) is the DC current. The first derivative can be seen as

j d S V

S

V I e I I G R

dV

dI 1

) ( ₀

0

0

=

= +

=

=

α

^α

α

which defines the junction resistance of the diode, R

j

, and the dynamic conductance of the diode, G

d

=1/R

j

. The second derivative is then expressed as

' 0

2 2

2 2

) (

0

0 0

d d S

V S V

d

V

G G I

I e

dV I dG dV

I

d = =

α

^α =

α

+ =

α

=

The V-I characteristic of the diode can now be rewritten as

2 ...

)

(

^'

2 0

0

+ = + + +

=

_d

v G

_d

vG I i I V I

and is thus the three-term approximation for the diode current [2].

2.7.2 Single-Ended Mixers

The single-ended mixer is the simplest type of mixers and is often used as a part in more complex mixers. If a RF signal is mixed in a downconverter with a signal from a local oscillator and the signals can be described as

) cos(

) (

) cos(

) (

t v

t v

t v

t v

LO LO

LO

RF RF

RF

ω ω

=

=

From the three-term approximation for the diode current it is possible to see that the diode current will consist of a DC current, the RF and local oscillator frequencies. The v

²

term will then give rise to the following output current.

35