Modeling of RF-design at board level for Assisted Global Positioning System (AGPS)

(1)

Department of Science and Technology

Institutionen för teknik och naturvetenskap

Linköping University Linköpings Universitet

SE-601 74 Norrköping, Sweden

601 74 Norrköping

LITH-ITN-ED-EX--07/020--SE

Modeling of RF-design at board

level for Assisted Global

Positioning System (AGPS)

Michael Paszowski

(2)

LITH-ITN-ED-EX--07/020--SE

Modeling of RF-design at board

level for Assisted Global

Positioning System (AGPS)

Examensarbete utfört i Elektronikdesign

vid Tekniska Högskolan vid

Linköpings unversitet

Michael Paszowski

Examinator Adriana Serban Craciunescu

Norrköping 2007-11-30

(3)

Upphovsrätt

Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare –

under en längre tid från publiceringsdatum under förutsättning att inga

extra-ordinära omständigheter uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,

skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för

ickekommersiell forskning och för undervisning. Överföring av upphovsrätten

vid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av

dokumentet kräver upphovsmannens medgivande. För att garantera äktheten,

säkerheten och tillgängligheten finns det lösningar av teknisk och administrativ

art.

Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman i

den omfattning som god sed kräver vid användning av dokumentet på ovan

beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan

form eller i sådant sammanhang som är kränkande för upphovsmannens litterära

eller konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press se

förlagets hemsida

http://www.ep.liu.se/

Copyright

The publishers will keep this document online on the Internet - or its possible

replacement - for a considerable time from the date of publication barring

exceptional circumstances.

The online availability of the document implies a permanent permission for

anyone to read, to download, to print out single copies for your own use and to

use it unchanged for any non-commercial research and educational purpose.

Subsequent transfers of copyright cannot revoke this permission. All other uses

of the document are conditional on the consent of the copyright owner. The

publisher has taken technical and administrative measures to assure authenticity,

security and accessibility.

According to intellectual property law the author has the right to be

mentioned when his/her work is accessed as described above and to be protected

against infringement.

For additional information about the Linköping University Electronic Press

and its procedures for publication and for assurance of document integrity,

please refer to its WWW home page:

http://www.ep.liu.se/

(4)

Institutionen för teknik och naturvetenskap

Department of Science and Technology

Examensarbete

Modeling of RF-design at board level for Assisted

Global Positioning System (AGPS)

Examensarbete utfört i Electrical Engineering vid Tekniska högskolan i Linköping

av

Michael Paszowski

LITH-ITN-ED-EX-07/020-SE

Norrköping 2007

Department of Science and Technology Linköpings tekniska högskola

Linköpings universitet Linköpings universitet

(5)

(6)

Modeling of RF-design at board level for Assisted

Global Positioning System (AGPS)

Examensarbete utfört i Electrical Engineering

vid Tekniska högskolan i Linköping

av

Michael Paszowski

Handledare: Peter Thellenberg

Infineon

Adriana Serban

itn, Linköpings universitet

Examinator: Adriana Serban

itn, Linköpings universitet

(7)

(8)

Avdelning, Institution

Division, Department

Institute of Technology and Science Department of Science and Technology Linköpings universitet

SE-601 74 Norrköping, Sweden

Datum Date 2007-11-30 Språk Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport

URL för elektronisk version

http://www.itn.liu.se

ISBN

—

ISRN

Serietitel och serienummer

Title of series, numbering

ISSN

—

Titel

Title

Modeling of RF-design at board level for Assisted Global Positioning System (AGPS) Författare Author Michael Paszowski Sammanfattning Abstract

This thesis describes the design of a 1575.42 MHz Low-Noise Amplifier (LNA) using a Hetero-Junction Field Effect Transistor (HJ-FET) from NEC. The LNA design focuses on a minimum noise figure and good power gain in order to improve receiver sensitivity. The first evaluation of the LNA module shows a good agree-ment between the simulated and measured results. However, the output matching section has some deviation from the reflection coefficient against the simulated results, which in turn led to a minor redesign of the output matching network.

Touchstone parameters representing a via and a SubMiniature version A (SMA) connector were extracted from measurements using Matlab and verified in Mi-crowave Office.

The LNA prototype has a measured gain of 15.54 dB, a noise figure of 0.80 dB. The receiver minimum detectable signal level with SAW-filter is decreased from -159.15 dBm using the Infineon BGA615L7E6327 Silicon Germanium GPS Low-Noise Amplifier to -159.40 dBm.

Nyckelord

(9)

(10)

Abstract

This thesis describes the design of a 1575.42 MHz Low-Noise Amplifier (LNA) using a Hetero-Junction Field Effect Transistor (HJ-FET) from NEC. The LNA design focuses on a minimum noise figure and good power gain in order to improve receiver sensitivity. The first evaluation of the LNA module shows a good agree-ment between the simulated and measured results. However, the output matching section has some deviation from the reflection coefficient against the simulated results, which in turn led to a minor redesign of the output matching network.

Touchstone parameters representing a via and a SubMiniature version A (SMA) connector were extracted from measurements using Matlab and verified in Mi-crowave Office.

The LNA prototype has a measured gain of 15.54 dB, a noise figure of 0.80 dB. The receiver minimum detectable signal level with SAW-filter is decreased from -159.15 dBm using the Infineon BGA615L7E6327 Silicon Germanium GPS Low-Noise Amplifier to -159.40 dBm.

(11)

(12)

Acknowledgments

Peter Thellenberg, supervisor and personal mentor whose support and technical knowledge was a benefit in giving me the clues needed to solve some problems.

Adriana Serban, examinator who has corrected pure fact errors, and giving pointers at layout.

Lars van der Klooster, Territory Manager Scandinavia-West and Benelux for Applied Wave Research Ltd. For an outstanding introduction to Microwave Office and continued support throughout the whole project.

(13)

(14)

List of Tables

4.1 Mean values of PCB dimensions and deviation, W is transmission line width. . . 11

6.1 List of the components used in the NEC evaluation board. . . 22

6.2 Transistor selection. . . 22

6.3 Comparison of results between simulations with ideal and real com-ponents. . . 23

6.4 List of the components used in the matching networks. . . 24

6.5 List of values for calculating transistor noise. . . 25

6.6 Recommended operating conditions for the NEC transistor (TA = +25°C). . . 29

6.7 DC bias network characteristics. . . 30

6.8 List of the components used in the bias network. . . 31

6.9 SAW filter B9000 characteristics. . . 32

(16)

Contents xi

6.11 Cascaded noise and gain, values from simulations. . . 34 7.1 Reference simulations and measurements, compared with NEC

ap-plication note. . . 39 7.2 Simulated gain and noise compared to measured results with the

network seen in Fig. 6.3 and table 6.4. . . 40 7.3 Simulated reflection coefficients compared to measured with the

net-work seen in Fig. 6.3 and table 6.4. . . 40 7.4 New output matching network values to counter the difference impedance

between simulations and measurements. . . 43 7.5 List of components for three different network configurations. . . 43 7.6 Measured gain and noise with the network seen in Fig. 6.3 and

table 6.4. . . 44 7.7 List of components in the input matching network to counter the

change in source impedance by the SAW filter. . . 44 7.8 Network configuration OMN change performance at different ID

currents. . . 46 7.9 1dB compression point, LNA Prototype versus the reference design

[1]. . . 46 7.10 System measurements. . . 49 7.11 Calculation cascaded gain and noise of individual measurements and

comparison against full measured system. . . 51 7.12 Calculation cascaded gain and noise of individual measurements and

comparison against full measured system with SAW filter enabled. 51 7.13 Comparison of minimum detectable signal level and corresponding

system noise figure. . . 52 8.1 List of components used in the LNA. . . 56 8.2 Gain and Noise figure, f = 1575.42 MHz and bias point ID = 9.7

mA, VDD= 2.0 V, TA= 25◦C. . . 56

List of Figures

2.1 The first stages of a GPS front-end. . . 3 2.2 GPS signal modulation. . . 4 2.3 Regular GPS versus A-GPS, courtesy of Global Locate. . . 5 3.1 How different reflection coefficients are defined for transistor

calcu-lations. . . 7 4.1 Mean value dimensions of the top layers. . . 12 4.2 Frequency response for a 5.775 mm trace (11 times the width),

measured and simulated. . . 13 5.1 Top part of the via test trace. . . 15

(17)

xii Contents

5.2 Matrix multiplying of scattering transfer matrices of two-ports, A

and B. . . 16

5.3 Full measurements versus cascaded individual component measure-ments with via (a,c) and SMA (b,d). . . 19

5.4 Problem with the calculated SMA model. . . 20

5.5 Losses in a via. . . 20

6.1 NEC GPS evaluation board schematics. . . 21

6.2 (a) Gain, (b) noise and (c) stability for the evaluation board using ideal components versus SPICE representations. . . 23

6.3 Networks, input matching on the left side and output on the right. 25 6.4 LNA design, simulation results: (a) Γ_opt for optimum noise figure and (b) ΓL for maximum gain. . . 26

6.5 Constant gain and noise circles. ΓS is marked with a brown diamond. 27 6.6 Frequency response of a 47 nH Murata inductor. . . 28

6.7 Basic DC bias network. . . 29

6.8 Current, gain and noise dependency taken from the data sheet. . 30

6.9 Final bias network. . . 31

6.10 S22 of SAW filter . . . 33

6.11 LNA layout with dimensions. . . 34

6.12 LNA simulation results for (a) Return loss, (b) Stability factor (µ1) and (c) Noise figure (cross) and gain (triangle). . . 35

7.1 A part of the HammerHead verification PCB layout. When only the LNA is measured the output is connected at the location marked EXTLNAOUT. . . . 38

7.2 Measurements with reference values in the networks, compared to simulations (Eval board all real). . . 39

7.3 Prototype design of LNA showing (a) Simulated (IMN) and mea-sured ΓS ,(b) Simulated (OMN) and measured ΓL and (c) Simu-lated and measured gain (rectangle and square respectively) and simulated noise figure (diamond). . . 41

7.4 Optimization of the OMN. ΓL before the optimization (gamma_l) and optimized ΓL (gamma_l_omn_change) . . . 42

7.5 ΓS, LNA module with SAW filter. . . 45

7.6 1dB compression point measurement (LabView). . . 47

7.7 Comparision of simulated and measured results of the LNA regard-ing (a) Input return loss, (b) Output return loss, (c) Gain with simulated noise factor and (d) Stability factor µ1. . . 53

8.1 LNA layout on the PCB. . . 55

8.2 LNA data of (a) Gain, (b) Input and Output Return Loss (double triangle and single triangle respectivly), (c) Stability Factor µ1and (d) Stability Factor µ1 with SAW filter at the input. . . 57

(18)

Contents xiii

(19)

(20)

Chapter 1 Introduction

The level this Master Thesis is written on requires good knowledge of electrical circuits and a familiarity with radio frequency (RF) theory and RF circuits. Basic RF theory and equations will be briefly explained in chapter 3, those already familiar with the these basics can skip this chapter.

1.1 Goals

The goal of the master thesis is to design a Low-Noise Amplifier for the Ham-merhead I AGPS chip from Infineon. The designed LNA must meet the following conditions:

• The noise figure should be near-to-minimum noise figure over the specified bandwidth

• Gain should exceed 15 dB over the specified bandwidth • The LNA should be stable from DC to 5 GHz

• The operating bandwidth is 1.574397 - 1.576443 GHz • Minimized layout of the footprint

Also, there are some additional assignments that have to be researched: • Create models of vias and SMA-connectors from measurements • Show how simulations and measurements correlate with each other

This design will be implemented on the verification board and compared with the existing external LNA from Infineon, the BGA615L7E6327.

(21)

2 Introduction

1.2 List of Abbreviations

AWR Applied Wave Research DUT Device Under Test Γ Reflection Coefficient GPS Global Positioning System

HJ-FET Hetero Junction Field Effect Transistor IMN Input Matching Network

IF Intermediate Frequency LNA Low-Noise Amplifier OMN Output Matching Network PCB Printed Circuit Board

PGC Programmable Gain Controller RF Radio Frequency

SAW Surface Acoustic Wave SNR Signal to Noise Ratio

1.3 Software

The software used was primarily the RF simulator Microwave Office from Applied Wave Research (AWR). Calculations were made in Matlab using the RF toolkit. For system measurements LabView was used to calculations.

1.4 Hardware

The components used in this project are:

Type Company Series

Inductor Coilcraft 0402CS

Inductor Murata LQG15HS

Capacitor Murata GRM1552C

Transistor NEC NE3509M04

SAW filter Epcos B9000

GPS chip Infineon Hammerhead-I

Printed Circuit Board (PCB) Laminate Isola FR-370HR The equipment used to verify the design are:

Type Company Model no

Vector Network Analyzer Rohde & Schwarz ZVB8, 300 kHz . . . 8 GHz Noise Figure Meter Hewlett Packard 8970B

Noise Source Agilent 346A

(22)

Chapter 2 Global Positioning System

(GPS) Front-end

The overall noise factor of the receiver front end is dominated by the first stages, as seen in [10]. The total noise ratio and gain ratio of the system shown in Fig. 2.1 are expressed by (2.1) and (2.2), where F is noise ratio and G is gain ratio.

F = F1+ F2− 1 G1 +F3− 1 G1G2 + F4− 1 G1G2G3 , (2.1) G = G1· G2· G3· G4, (2.2)

Equation (2.1) shows how important it is to have a low noise ratio and at least

Figure 2.1. The first stages of a GPS front-end.

a moderate gain in the first stages since later stages have a diminishing impact on overall noise performance. The SAW B9000 is a band pass filter which only lets the GPS frequency pass. The "1st LNA" is the one which is designed in this rapport. Since the entire Hammerhead chip is based on a balanced design a balun is required to transform the unbalanced signals to balanced. The last component is the internal LNA ("2nd LNA"), which is an LNA combined with a mixer.

(23)

4 Global Positioning System (GPS) Front-end

2.1 Global Positioning System Background

Currently, there are 30 GPS satellites in service. The first satellites were launched in 1978 (although none of these are in service today). The carrier center frequency of the GPS system i 1575.42 MHz with a bandwidth of 2.046 MHz [11]. A GPS receiver calculates it’s position by measuring the distance between itself and tree or more GPS satellites. By measuring the time delay between transmission and reception the receiver can calculate the distance to each satellite. Once the receiver knows the position of, and distance to, at least three satellites, it can compute its position using trilateration. The key element for accuracy is clock synchronization. The receiver usually tracks a satellite and synchronizes its own clock with their atomic clock.

Figure 2.2. GPS signal modulation.

2.1.1 Assisted GPS

Assisted GPS, or A-GPS, was introduced to enhance the performance of the GPS. Conventional GPS receivers have difficulties providing reliable positions in poor signal conditions. In addition, when first turned on, they must find a satellite and track it for a certain time to be able to download the almanac and ephemeris. An A-GPS receiver can address these problems, using an Assisted Server[6]. The assistance server has the ability to access information from the reference network, and also has computing power far beyond that of the GPS receiver.

(24)

2.1 Global Positioning System Background 5

(25)

(26)

Chapter 3 Low-Noise Amplifier Design

3.1 Reflection Coefficient Definition

The parameter Γ is called the reflection coefficient, and shows what fraction of an applied signal is reflected when a Z0 source drives a load of ZL [7]. When two

terminations are facing each other, the voltage reflection coefficient is computed as

ΓL=

ZL− Z0∗

ZL+ Z0

. (3.1)

When applying this to reflection coefficients concerning matching for minimum noise figure or maximum power gain, the definitions from Fig. 3.1 are:

ΓS Reflection coefficient at the output of the input matching network

Γ_in Reflection coefficient at the input of the transistor Γ_out Reflection coefficient at the output of the transistor

ΓL Reflection coefficient at the input of the output matching network

Figure 3.1. How different reflection coefficients are defined for transistor calculations.

(27)

8 Low-Noise Amplifier Design

3.2 Noise

Noise plays a major role in determining the overall performance of a receiver, because, with the signal power, it enters as the Signal to Noise Ratio (SNR) into fundamental equations that determine the data rate of the system and the minimal signal level that can be received [8]. The fundamental definition of noise ratio F is, F = Si/Ni So/No = 1 +TA TR , (3.2)

where Sn is signal power at input or output, Nn noise power, TA component

effective noise temperature and TR ambient temperature. Typically, it is more

convenient to show noise ratio in dB, introducing the quantity noise figure:

N F = 10 log₁₀F dB. (3.3)

The noise of a receiver system has various sources and characteristics:

• The noise produced by the antenna is usually modeled as additive, white Gaussian noise and is thermal in nature

• The filter band limits the signal but has some insertion loss and therefore thermal noise contribution

• The transistor, which contribute thermal noise, shot noise and 1/f noise

3.2.1 Noise Temperature

Any electrical conductor contains electrons which are free to move around, more in good conductors and less in near-isolators. At normal temperatures, the electrons are in random motion, although on average there is no net force unless an electric field is added. This random motion of electrons can be detected as random noise [13].

Thermal noise is expressed:

PN = kT B, (3.4)

where PN is noise power, k is the Boltzmann’s constant, T temperature in kelvin

and B the bandwidth of the system. The thermal noise generated by a resistor at room temperature is 1.38 × 10−23× 290 × B W. PN is not dependent on the

ohmic value of the resistor.

There are many types of electrical noise and most of them are not truly thermal in origin. However, all types of random noise can be expressed as the equivalent amount of thermal noise that would be generated at a component effective noise temperature TA[13].

The level of noise sets the floor where the minimum signal level can be detected. Practically speaking, if the noise floor is very low in the GPS system, this means that the user will be able to pick up a weak signal, i.e. inside buildings, and still be able to know the position. The easiest variable to change in (3.4) to lower noise

(28)

3.3 Amplifier Design for Optimum Power Gain 9

is the bandwidth (B). A narrow bandwidth of the system is proffered for a lower noise [8].

Finally, the lowest signal level (noise floor) the receiver can detect and amplify is

PN|in = kT BF. (3.5)

3.2.2 Amplifier Design for Minimum Noise Figure

The total noise output of a two-port is highly dependent on the source impedance. A unique optimum source impedance, Z_optexists, that leads to the best noise per-formance (Fmin). This is found by applying a variable source impedance, and then

converting it to a optimum noise reflection coefficient, Γ_opt. A sensitivity factor is also added in the total noise equation, Rn, and is called the equivalent noise

resistance. Rn shows how fast the noise figure increases as the source termination

changes from Γopt [7].

The total noise of a two-port is: F = Fmin+ 4Rn Z0 |ΓS− Γopt| 2 1 − |ΓS| 2 |1 + Γ_opt|2 . (3.6)

Minimum noise is achieved when ΓS = Γopt.

3.3 Amplifier Design for Optimum Power Gain

An amplifier is designed for maximum gain if

ΓS = Γ∗_In (3.7)

and

ΓL= Γ∗_Out. (3.8)

Obviously, maximum gain cannot be achieved when LNA must be designed as the input matching network is determined by ΓS = Γopt∗ and Γopt6= Γin. Since the

real-world transistors are bilateral transistors, |S12| 6= 0, the LNA design requires

a simultaneous conjugate match condition implemented with the input matching network (IMN) and the output matching network (OMN). However, for minimum noise figure amplifier design, the specific condition is ΓS = Γopt∗ and it is the

start point of the design. Using the Microwave Office simulation tool GM2, the design of the LNA becomes an optimization process of the IMN and OMN under the condition of amplifier stability [10].

Γ∗S= S11+ S12S21ΓL 1 − S22ΓL , (3.9) Γ∗_L= S22+ S12S21ΓS 1 − S11ΓS . (3.10)

These equations can be simplified further, but since Microwave Office has the parameter GM2, Simultaneous Match at Output, the steps required are simply to

(29)

10 Low-Noise Amplifier Design

connect the input matching network and make the device stable to be able to read ΓL [10].

The most useful gain definition for amplifier design is the transducer power gain, which accounts for both source and load mismatch. It is denoted GT in Microwave Office, and can be seen in (3.11)[10].

GT = PPower delivered to the load

PPower available from source = |S21| 2 1 − |ΓS| 2 1 − |ΓL| 2 |1 − ΓSΓIn| 2 |1 − S22ΓL|2 (3.11)

3.3.1 Gain Compression

If the input signal of an amplifier is

vi= Vicos ω0t, (3.12)

the output voltage can be approximated by

vo= a0v0i + a1v1i + a2vi2+ a3v3i + . . . . (3.13)

The result leads to the voltage gain of a signal component at frequency ω0:

Gv= v(ω0) o v(ω0) i = a1Vicos ω0t + 3 4a3V 3 i cos ω0t Vicos ω0t = a1+ 3 4a3V 2 0 (3.14)

where only the third order term is retained. The term a3 is normally negative,

so that the gain of the amplifier will decrease for larger values of V0. This effect

is called gain compression. It is mostly due to a limitation of the supply voltage used to bias the device. The 1dB compression point is used to quantify the linear range of the amplifier. The point is referenced where the power level for which the output power has decreased by 1 dB from the ideal characteristic [10].

3.4 Stability

There are several ways of computing the stability factor, the one used in the sim-ulations were µ1, (denoted MU1 in Microwave Office). µ1computes the geometric

stability factor of a 2-port [10]. The geometric stability factor computes the dis-tance from the center of the Smith chart to the nearest unstable point of the output load plane [9]. The necessary and sufficient condition for unconditional stability of the two port is that µ1 > 1. In addition, greater values of µ1 implies greater

stability. The stability factor is computed from

µ1= 1 − |S11| 2 |S22− ∆S11∗| + |S12S21| (3.15) where ∆ = S11S22− S12S21. (3.16)

(30)

Chapter 4 The PCB Laminate

The laminate used in this project is the FR-370HR Laminate from Isola. It is not in any way an RF specialized laminate with low dielectric loss and flat response, but for GPS applications it will suffice and lower the cost. The constants that are required when defining a substrate in Microwave Office are:

r 4.04 Relative dielectric constant

H 0.258 mm Substrate thickness T 0.057 mm Conductor thickness

ρ 0.75 Metal bulk resistivity normalized to gold Tand 0.021 Loss tangent of dielectric

r and Tand can be found in Isolas data sheet [5], while ρ has to calculated (the

metal used is copper), and the rest measured. Due to process variations, it is important to follow up and measure the PCB to verify that everything is correct.

Table 4.1. Mean values of PCB dimensions and deviation, W is transmission line width.

Parameter Mean value (mm) Deviation from 2nd largest/smallest value

H 0.258 1.47%

T 0.057 8.77%

W 0.509 1.16%

In order to see the variation and have a good average value, 11 measurements per parameter in different places were measured. The highest and lowest values were subtracted and a mean value was calculated. The deviation per cent-age was calculated by dividing the biggest difference between the second largest, or the second smallest value, with the mean value (see table 4.1).

By inserting the electrical and mechanical values of the substrate it is possible to calculate the required width to create a 50 Ω transmission line in txline; the line width required is calculated to be 0.502 mm. Another important factor to consider is the frequency response of the laminate. Since Microwave Office cannot handle

(31)

12 The PCB Laminate

Figure 4.1. Mean value dimensions of the top layers.

frequency dependent substrate, the only way to find out the frequency response is to measure the trace. As seen in Fig. 4.2, the measured and simulated traces follow quite well, up to 3 GHz. Beyond this frequency, the measured trace starts to deviate very much against the simulated response. These results are repeatable for different lengths, all show the same degradation in performance beyond 3 GHz. The findings are confirmed by Isola.

In practice this means that the simulated model will not correspond very well if this particular laminate is used for frequencies beyond 3 Ghz. Not only is a higher loss expected, but the values of the matching networks might as well have to be changed. But, since the measurements correspond to each other at least to 1.575 GHz, there is no reason to assume that the final results will deviate due to the laminate.

(32)

13

Figure 4.2. Frequency response for a 5.775 mm trace (11 times the width), measured

(33)

(34)

Chapter 5 Modeling Individual

Components

The via and SMA connector were the two components that were to be character-ized. Two test networks were printed on PCB and measured. By being able to measure the connecting strip lines (especially in the via network) it was possible to extract the wanted Touchstone parameters for the via and SMA-connector.

Figure 5.1. Top part of the via test trace.

(35)

16 Modeling Individual Components

5.1 Scattering Parameters

The measurement results when using a network analyzer are the S-parameters which characterize the device under test (DUT) at a specified bias condition. The S-parameters are power wave descriptions that define the input-output relations of a network in terms of incident and reflected power waves [12]. When trying to calculate individual elements of a cascaded network it is desirable to be able to do matrix multiplications in order to solve the unknown elements.

5.2 The Cascadable Scattering Transfer Matrix

To extend the concept of S-parameter representation to cascaded networks, it is more efficient to rewrite the power wave expressions arranged in terms of input and output ports [12].

a_A1 b_A1 = T_A11 T_A12 TA21 TA22 b_A2 a_A2 and a_B1 b_B1 = T_B11 T_B12 T_B21 T_B22 b_B2 a_B2 (5.1) Looking at fig. 5.2 the traveling wave vector at the output stage of A is the same

Figure 5.2. Matrix multiplying of scattering transfer matrices of two-ports, A and B.

vector at the input stage of B. b_A2 a_A2 = a_B1 b_B1 = T_B11 T_B12 T_B21 T_B22 b_B2 a_B2 (5.2) Combining (5.1) and (5.2) yields:

a_A1 b_A1 = T_A11 T_A12 T_A21 T_A22 T_B11 T_B12 T_B21 T_B22 b_B2 a_B2 . (5.3)

Or in a simpler matrix form:

(36)

5.3 Via and SMA-connectors Modeling Using Matlab 17

Converting from S-parameters to T-parameters and vice versa: T11 T12 T21 T22 = 1 S21 1 −S22 S11 −DET [S] (5.5) S11 S12 S21 S22 = 1 T11 T21 DET [T ] 1 −T12 . (5.6)

5.3 Via and SMA-connectors Modeling Using

Mat-lab

Although it’s easy in theory to solve the equations and have a solution, doing it in practice was a lot more difficult. The equations for the via and SMA connector were as follows:

Tres = Ttoptrace· Tvia· Tbottomtrace· Tvia· Ttoptrace (5.7)

Tres = Tsma· Ttrace· Tsma (5.8)

Solving T_VIA and T_SMA would render in four unique solutions, ±Re(Tnm) ±

Im(Tnm), unfurtunatly Matlab was not able to solve the system, with four

equa-tions and four unknowns. Next step was to try to solve the system expressed only in two unknown variables. The reason why this can be made is because the symmetry of the setup should ideally result in S11 = S22 and S12 = S21. The

simplification that was made was:

Unknown matrix = S11 S12 S21 S22 = S11 S12 S12 S11 ⇒T " 1 S12 − S11 S12 S11 S12 (−S2 11+S122) S12 # , (5.9) where the matrix on the right hand side in (5.9) is the T-parameter representation. In addition, the measured S-parameters were also recalculated in order to make the differences in values insignificant.

S11 S12 S21 S22 = S11+S22 2 S12+S21 2 S12+S21 2 S11+S22 2 (5.10) Only two solutions were created for the via and SMA connector, both of them identical.

5.3.1 Matlab Limitations and Problems

Matlab seemed to have some trouble handling large matrices, as it sometimes could not find a solution at frequency t = 396, but a solution could be found if starting from 395 instead of 1. A workaround was created to handle the large matrices; by using measurements that had narrower frequency band (1.0 - 2.0 GHz instead of 0.03 - 5 GHz). But then a new problem arose, Matlab could not handle too large

(37)

integers before converting them. This problem was never solved, but the integer overflow happened furtunatly at the the end of the data, rendering the last seven of 400 frequencies unsolved. A quick work around was to duplicate the last known frequency solution to the missing seven (see end of appendix B). When the SMA connector was put in the same network from which it was calculated from, the results are the same as the entire system. But due to a calculation error there is an inconsistently at 1.122 GHz, which can only be seen when simulating one SMA-connector, see Fig. 5.4. The via on the other hand does not experience these problems, see Fig. 5.5.

(38)

5.3 Via and SMA-connectors Modeling Using Matlab 19

(a) (b)

(c) (d)

Figure 5.3. Full measurements versus cascaded individual component measurements

(39)

Figure 5.4. Problem with the calculated SMA model.

(40)

Chapter 6 Design of a 1.575 GHz

Low-Noise Amplifier

A Low-Noise Amplifier (LNA) is used as a preamplifier in receiver applications, where the noise figure and the gain of the first active circuit, i.e., the LNA, de-termine the receiver sensitivity. In this chapter the design of an LNA for GPS systems will be presented.

6.1 Transistor Selection

Figure 6.1. NEC GPS evaluation board schematics.

(41)

22 Design of a 1.575 GHz Low-Noise Amplifier

Table 6.1. List of the components used in the NEC evaluation board.

Symbol Value C1 51 pF C2 10 000 pF C3 1000 pF C4 1000 pF C5 10 pF L1 10 nH L2 4.7 nH L3 4.7 nH R1 30 kΩ R2 20 Ω R3 150 Ω

The transistor which was selected to be implemented on the design is a Hetero Junction Field Effect transistor from NEC, NE3509M04. The specifications for the transistor are taken from [2]. NEC has released an evaluation board which is

Table 6.2. Transistor selection.

Gain (dB) Noise (dB) Condition

Transistor only 17.5 0.4 f = 2 GHz, VDS = 2 V, ID = 10 mA

Evaluation board 16.7 0.68 f = 1.575 GHz, VDD = 2 V, ID = 9.4 mA

designed using the NE3509M04 in a GPS system, operating at 1.575 GHz. The design and components used in the evaluation board can be seen in Fig. 6.1. Un-fortunately the NEC evaluation board could not be measured at Infineon, so the noise and gain data are taken directly from the data sheet [1]. The next step was to set up a project in Microwave Office and insert the "real" components to see if the results could be close. Microwave Office has an extensive library consisting of many vendors components. The components that are used on the GPS board from Infineon are primarily from Coilcraft, the 0402CS-series of inductors, and from Murata, LQG15HS (inductors) and GRM1552 (capacitors). Ideal compo-nents used in simulations have a corresponding impedance which is independent of frequency and no parasitics, as opposed to using real components from the vendors (see table 6.3 for results from the simulations). A comparison between simulations of ideal and modeled components of the evaluation board will be pre-sented (for more detailed data see Fig. 6.2): The transmission line dimensions of the evaluation board were measured and used in the real simulation.

(42)

6.1 Transistor Selection 23

(a) (b)

(c)

Figure 6.2. (a) Gain, (b) noise and (c) stability for the evaluation board using ideal

components versus SPICE representations.

Table 6.3. Comparison of results between simulations with ideal and real components.

Ideal comp. Real comp.

Noise Figure 0.42 dB 0.56 dB

(43)

6.2 Improving the Evaluation Board

The LNA design presented in this section should improve the typical 1.575 GHz NEC reference design in terms of noise figure, gain and stability. The gain and noise figure for every amplifier are dependent on each other, being subjects of trade-offs on system level design. For results from the simulations see section 6.6.

6.2.1 Networks

Input Matching Network

When designing a Low-Noise Amplifier there will always be a trade-off between noise figure and gain of the amplifier. The goal was to improve the evaluation board, in terms of both gain and noise. The resulting gain noise ratio before entering the Hammerhead chip is in the end determined of how the cascaded noise in (2.1) turns out. The key idea behind creating the low-noise part of a LNA is to create an input matching network which transforms from the 50 Ω (Z0) source

impedance to an impedance corresponding to Γ_opt, the optimum source reflection coefficient (section 3.2.2 and [12]).

As seen in table 6.4 two types of inductors were used, Coilcraft and Murata. The major differences between these two are 1) that the Coilcraft are more ex-pensive than the Murata and 2) Coilcraft generates lesser noise (higher Q-value). Coilcraft was therefore used when the inductor was in series with the RF signal. Equation 3.6 shows the noise of the transistor based on the source reflection coef-ficient, ΓS, of the input matching network. The input network that was created

can be seen to the left of the transistor in Fig. 6.3 and the reflection coefficients in Fig. 6.4 (a). Not surprisingly, the input matching network that was created has more or less the same values as the evaluation board. The resistor was replaced by an inductor (L1), since this acts as a low pass filter, and will make the device more stable at lower frequencies. The values for ΓS and Γopt can be found in Fig. 6.4

and table 6.5, as well as Rn and Fmin. When the values in table 6.5 are inserted

Table 6.4. List of the components used in the matching networks.

Symbol Value Vendor Model no

C1 47 pF Murata GRM1555C1H470JZ01 L1 47 nH Murata LQG15HS47NJ02 L2 11 nH Coilcraft 0402CS-11NX_BG L3 4.3 nH Coilcraft 0402CS-4N3X_BG L4 47 nH Murata LQG15HSR12J02 C2 4.7 pF Murata GRM1555C1H4R7JZ01 R1 130 Ω KOA

in (3.6) the calculated result is 0.28 dB, while the total noise for the LNA is 0.55 dB. It is reasonable to assume that the 0.27 dB in noise difference is generated by the transmission lines and the lumped components [4].

(44)

6.2 Improving the Evaluation Board 25

Figure 6.3. Networks, input matching on the left side and output on the right. Table 6.5. List of values for calculating transistor noise.

Parameter Value

Fmin 0.276 dB

ΓS 0.7436∠30.78

Γopt 0.7805∠27.22

Rn 9.0125 Ω

Output Matching Network

The output matching network (OMN) is the only network in a LNA that can determine the gain of the transistor, since the input matching network is designed for minimum noise. For maximum gain the output port of the transistor is the conjugate of the input port of the output matching network (see section 3.3). Fig. 6.4 (b) shows the calculated conjugate match (GM2) and the ΓL impedance

(45)

(a) (b)

Figure 6.4. LNA design, simulation results: (a) Γoptfor optimum noise figure and (b)

(46)

6.2 Improving the Evaluation Board 27

6.2.2 A Discussion of Trade-offs Between Noise and Gain

The easiest way to describe the noise and gain dependency is with constant gain and noise circles, which can be seen in fig 6.5. The maximum stable gain of the

Figure 6.5. Constant gain and noise circles. ΓSis marked with a brown diamond.

NE3509N04 at 1.575 GHz is 18.9 dB. At this gain the device has a rated noise of 0.38 dB, which would result in a final noise figure of 0.65 dB, if the same noise of 0.27 dB from the networks is added. If ΓS is changed to the value corresponding

to the point 0.57∠43.15, which can be achieved by using a 6.7 nH inductor for L2, the resulting noise can be confirmed to be 0.62 dB. The output network was not altered, which in effect means that there could be more losses in the output stage with changed values to have a simultaneous output match. However, having these new characteristics is not wanted due to the following reasons:

• The high gain can interfere with the next stage of the receiver, with signal power exceeding the compression point and cause harmonic distortion [10] • The cascaded noise figure for the entire system will increase from 1.42 to 1.47

(47)

6.3 Stability

In Fig. 6.3, there are three components that impact on stability: L1, L4 and R1. A decreased value of R1 will improve the overall stability as it introduces a loss in the network. L1 and L4 are RF-block elements. Their nominal value is 47 nH and their frequency response (S21) can be seen in fig 6.6. If the value of L1 is lowered

more losses will be presented to to network, since the RF signal will be leaking to the ground node, thus increasing stability but lower gain. If L4 is lowered the system has a tendency to become unstable, since RF signals will leak into the bias network. In the current state they act as a band pass filter.

(48)

6.4 Bias Network 29

6.4 Bias Network

The purpose of DC bias design is to select the proper quiescent point and hold the quiescent point constant over variations in transistor parameters and temperature [4]. There are two types of bias networks; active and passive. Active networks employ several transistors and are more complex to design but they can result in a smaller dependence of the amplifier parameters, concerning temperature and transistor parameters variation. Passive (or self-biased) networks are the simplest and incorporate a resistor network to find the desired quiescent point [12]. In this design the passive bias network is chosen due to its simplicity. Table 6.6 shows the recommended operating conditions for the transistor, although a smaller VDS

was chosen since the Application Note [1] has 2 V as VDD.

Table 6.6. Recommended operating conditions for the NEC transistor (TA = +25°C).

Parameter Symbol MIN. TYP. MAX. Unit

Drain to Source Voltage VDS − 2 3 V

Drain Current ID − 10 20 mA

Figure 6.7. Basic DC bias network.

There are various networks that can be employed for a DC bias network, but since there is only a single positive voltage source to the LNA, there is basically only one way to make a passive bias network [4], see fig 6.7 and table 6.7. The source resistor RS will provide automatic transient protection. The trade-off however, is

that it will at the same time degrade the noise-figure performance, and the source bypass capacitor can cause low-frequency oscillations. As seen in the reference network (Fig. 6.1), the source network has added an inductance and capacitance to filter out transients that may occur. This same filtering network is also used

(49)

Table 6.7. DC bias network characteristics.

Amplifier Power

characteristics supply used Low noise Unipolar, High gain incorporating High power RS gives

Lower efficiency automatic Gain easily adjusted transient by varying RS protection.

in the final design. If the bias network is not fed with the exact voltage that is required, a resistor in series with the voltage source can be added to lower the voltage. The values of these two resistors can be easily calculated with Ohm’s law, by tuning or by implementing the optimization routine in the Microwave Office environment to achieve desired VDS, VG and ID values. As seen in table 6.7 it is

Figure 6.8. Current, gain and noise dependency taken from the data sheet.

stated that varying RS the gain can be changed, this is true because the gain and

(50)

6.4 Bias Network 31

Figure 6.9. Final bias network.

Table 6.8. List of the components used in the bias network.

Symbol Value C3 1000 pF C4 10 000 pF C5 1000 pF L5 4.7 nH R2 22 Ω R3 51 Ω U1 2.5 V

(51)

6.5 SAW Filter

SAW filters are very effective band pass filters, as they are a direct analog imple-mentation of the finite impulse response filter [8], which in turn means that they have very sharp cutoff characteristics. The LNA has an unbalanced SAW filter to the input port, the B9000 from Epcos. According to the data sheet [3], the SAW filter does not require any network matching since it has 50 Ω impedance at both input and output ports. In reality, these impedances can be different. As seen in

Table 6.9. SAW filter B9000 characteristics.

min. typ. max.

Center frequency − 1575.42 − MHz

Maximum insertion attenuation

1574.42 MHz . . . 1576.42 MHz − 0.5 0.9 dB Amplitude ripple 1574.42 MHz . . . 1576.42 MHz − 0.0 0.3 dB Absolute attenuation 500.0 MHz . . . 894. MHz 16 18 dB 894.0 MHz . . . 1500.0 MHz 15 17 dB 1650.0 MHz . . . 4000.0 MHz 18 20 dB 4000.0 MHz . . . 6000.0 MHz 15 20 dB

table 6.9 the rejection of signals outside the pass band is excellent.

In order to use the SAW filter as a pre-select filter int the GPS front-end module design, the S22of the SAW filter was measured. The measurement results

can be seen in Fig. 6.10. Since the input matching network is created for a 50 Ω source impedance, the different impedance of the SAW filter will result in poorer matching at the input of the LNA. This can result in more noise and smaller gain of the whole LNA RF module.

(52)

6.5 SAW Filter 33

(53)

6.6 Simulation Results

Using (3.11) to calculate the transducer gain with the reflection coefficients stated in table 6.10, the calculated transducer gain is 16.52 dB. The simulations show a lower gain, this is due the fact that Microwave Office does cascaded complex computations for every block and takes into consideration higher order frequency reflections. The dimensions of the layout can be seen in fig 6.11. Emphasis was

Table 6.10. Coefficients used to calculate transducer gain.

Parameter Value ΓS 0.7426∠30.9 Γ_In 0.7327_{∠ − 34.13} ΓL 0.3419∠92.79 S22 0.5446∠ − 9.385 S21 4.855∠120.6

put on making the block as small as possible. As it stands now, the only possibility for making the design smaller is by using 0201 components.

Figure 6.11. LNA layout with dimensions.

Table 6.11. Cascaded noise and gain, values from simulations.

Gain (dB) Noise (dB) SAW B9000 -0.7 0.7 LNA 16.09 0.55 Balun -1 1 LNA II 79.5 4.08 Cascaded System 93.89 1.45

(54)

6.6 Simulation Results 35

(a) (b)

(c)

Figure 6.12. LNA simulation results for (a) Return loss, (b) Stability factor (µ1) and

(55)

(56)

Chapter 7 Measurement Results

Early in the design process of the new 1575 MHz LNA, the reference design in form of an evaluation board using the transistor NE3509MO4 released by NEC was analyzed. In this chapter the measurements results of the NEC reference design are presented. Differences between the expected values (given by [1]) of the LNA parameters e.g. gain and noise figure and the measured values are compared. The layout and network values of the evaluation board were changed in simu-lations to achieve a higher gain, better noise figure and improve stability; the LNA prototype. From section 7.2 to 7.3.2 this configuration was optimized in order to further improve gain and noise figure.

A note on displayed results in this section, excluding section 7.5

When measurements are displayed in tabular format, the gain and noise readings are from the 8970B Noise Figure Meter from HP. For a more detailed description on how gain and noise are calculated see appendix C.

When measurements are displayed in rectangular and Smith Chart format, the readings are from the ZVB8 Vector Network Analyzer from Rohde & Schwarz. ΓS and ΓLmeasurements are probed with the Cascade Microtech probe with the

input / output terminated with a 50 Ω SMA connector. All other measurements are done with standard SMA connectors.

Since the length of the transmission lines on the PCB are much longer than in the original simulated design (see Fig. 7.1), the incoming transmission lines where elongated to 12 mm and the outgoing to 25.1 mm in the simulations in order to match the PCB design. This is why the simulated results in this section

have lower gain, higher noise and different reflection coefficients than in previous sections. The longer transmission lines has a negligible effect on

system impedance since they are at the 50 Ω connectors, but does impact in gain and noise figure performance.

(57)

38 Measurement Results

Figure 7.1. A part of the HammerHead verification PCB layout. When only the LNA

(58)

7.1 Measurements of the Reference Design (NEC Evaluation Board) 39

7.1 Measurements of the Reference Design (NEC

Evaluation Board)

Early in the design process the reference network values and configuration from NEC was dismissed due to the bad performance from the simulations. In order to verify the findings the reference network was measured, see table 7.1 and Fig. 7.2. The measurements confirms the initial assessment with poor performance compared to what NEC states in the application note. As mentioned earlier, the application board was not available for testing.

Table 7.1. Reference simulations and measurements, compared with NEC application

note.

Gain (dB) Noise Figure (dB)

NEC Application Note 16.70 0.68

Simulated 14.32 0.78

Measured 14.48 0.85

Figure 7.2. Measurements with reference values in the networks, compared to

(59)

7.2 Measurements of the Prototype Design

Initial measurements of the LNA prototype were done to confirm the validity of the simulated results, see table 7.2, 7.3 and Fig.7.3. The difference between the measured and simulated gain can be explained by: 1) the change of ΓL seen in

table 7.3, and 2) by a different bias current, see section 7.3.2. At this point no steps were taken to change the output matching network, since the added presence of the SAW filter may very well change the input impedance.

Table 7.2. Simulated gain and noise compared to measured results with the network

seen in Fig. 6.3 and table 6.4.

DUT Gain (dB) Noise Figure (dB)

LNA Simulation 15.77 0.72

LNA Prototype 15.33 0.80

Table 7.3. Simulated reflection coefficients compared to measured with the network

seen in Fig. 6.3 and table 6.4.

Reflection coefficients Simulated Measured

ΓS 0.745∠31.24 0.7471∠34.58

(60)

7.2 Measurements of the Prototype Design 41

(a) (b)

(c)

Figure 7.3. Prototype design of LNA showing (a) Simulated (IMN) and measured ΓS ,(b) Simulated (OMN) and measured ΓLand (c) Simulated and measured gain (rectangle and square respectively) and simulated noise figure (diamond).

(61)

7.2.1 Optimization of the Output Matching Network of the

LNA Prototype

As seen in fig 7.3 (b) the ΓLof the LNA differs from the from the simulated value.

The ΓL required for simultaneous conjugate match is with SAW filter 0.31∠85.6

and 0.31_{∠100 without (these are simulated results, where the change in input} impedance that the SAW filter presents also changes the simultaneous conjugate match). 0.32∠90 was the closest possible point that could be created, which can be considered as a good average that will work well both with, and without, the SAW filter. Since only the output matching network is changed the resulting noise should be the same as in the network configuration named "standard".

Figure 7.4. Optimization of the OMN. ΓL before the optimization (gamma_l) and optimized ΓL(gamma_l_omn_change)

(62)

7.3 LNA Prototype Measurements including the SAW Filter 43

The optimized OMN results in new nominal values of L3, L4 and C2. These values are presented in table 7.4. The new value of ΓL is shown in Fig. 7.4. Since

only the OMN network was changed, the noise figure was not affected.

Table 7.4. New output matching network values to counter the difference impedance

between simulations and measurements.

Symbol Old value New value

L3 4.3 nH 3.3 nH

L4 47 nH 7.5 nH

C2 4.7 pf 3.9 pF

7.3 LNA Prototype Measurements including the

SAW Filter

The addition of the SAW filter in the networks was anticipated to create a different results in impedance, thus changing ΓS. The change in ΓS when adding the SAW

filter can be seen in Fig. 7.5. As seen in table 7.6 the gain doesn’t drop as much as the noise gets higher in the standard configuration, this can be explained by the fact that ΓS is shifted toward more gain.

In an attempt to bring order to the different network configurations that were designed and measured in this section, a list of values of the networks are presented in table 7.5. Standard denotes the networks that were designed in section 6.2.1.

Table 7.5. List of components for three different network configurations.

Symbol Standard IMN change OMN change Input C1 47 pF 4.7 pF 47 pF L1 47 nH 12 nH 47 nH L2 11 nH 13 nH 11 nH Output L3 4.3 nH 4.3 nH 3.3 nH L4 47 nH 47 nH 7.5 nH C2 4.7 pF 4.7 pF 3.9 pF R1 130 Ω 130 Ω 130 Ω

(63)

Table 7.6. Measured gain and noise with the network seen in Fig. 6.3 and table 6.4.

Measured Gain (dB) Noise Figure (dB) Network configuration

LNA 15.33 0.80 Standard

LNA 15.40 0.80 OMN change

SAW + LNA 14.90 1.50 Standard

SAW + LNA 14.40 1.40 IMN change

SAW + LNA 14.60 1.40 IMN + OMN change

SAW + LNA 15.15 1.50 OMN change

7.3.1 LNA Prototype Optimization of the Input Matching

Network with Connected SAW Filter

Since the ΓS point was changed in the presence of the SAW filter, the transistor

did not work in minimum noise mode. In an attempt to further lower the noise, the input matching network was redesigned to make the noise generated by the transistor as small as possible. The new network values of the IMN are presented in table 7.7, and the ΓS point can be verified in Fig. 7.5. As seen in table 6.9 the

attenuation of the SAW filter is between 0.5 and 0.9 dB. This attenuation is added as supplementary noise and loss in gain of the LNA. In the measurement where the transistor generates lowest noise possible the attenuation from the SAW filter is 0.6 dB (counting from the noise).

Table 7.7. List of components in the input matching network to counter the change in

source impedance by the SAW filter.

Symbol Old value New value

C1 47 pF 4.7 pF

L1 47 nH 12 nH

L2 11 nH 13 nH

The high loss in gain is dependent on two factors: 1) the previous ΓS point

(before the re-match) was situated in a region with more gain, compare fig 6.5 and 7.5, and 2) lowering the value will allow RF signals to leak into the ground node as discussed in section 6.3. Although not presented here, the simulated response when the inductor at the IMN is changed also show a decrease in gain and noise. In an attempt to increase the gain the output matching network was replaced with the configuration "OMN change". Unfortunately the gain didn’t exceed 15 dB in this configuration either.

(64)

7.3 LNA Prototype Measurements including the SAW Filter 45

(65)

7.3.2 Bias Network

All measurements that has been done so far have had the resistor R3 at the DC input shorted, since the LNA was fed with a 2 V source. Simulations show that ID should be 10.2 mA with a 2 V source with R2 at 22 Ω. The measurements

however, have a bias current that is lower than simulated, 8.3 mA. This means in effect that if the current is raised both gain and noise figure will improve (see Fig. 6.8). The network configuration which performed best in terms of gain and noise ratio ("OMN change") had R2 replaced from 22 Ω to 17.7 Ω, and the results can be seen in table 7.8.

Table 7.8. Network configuration OMN change performance at different IDcurrents.

Measured Gain (dB) Noise Figure (dB) ID

LNA 15.40 0.80 8.3 mA

LNA 15.54 0.80 9.7 mA

SAW + LNA 15.15 1.50 8.3 mA

SAW + LNA 15.35 1.50 9.7 mA

7.4 Measurement of the LNA Prototype 1 dB

Compression Point

The DUT was the LNA prototype which had the OMN change and was operating at ID= 9.7 mA. Figure 7.6 shows the 1dB compression point at the input (CP1)

and the gain at that point. Table 7.9 shows a comparison between the NEC Application Note and the Designed LNA. The results are not directly comparable, since the LNA in the Application Note is biased with a lower current (9.4 mA compared to 9.7 mA), see section 3.3.1 for an explanation why.

Table 7.9. 1dB compression point, LNA Prototype versus the reference design [1].

P1dBout

LNA Prototype 7.90 dBm NEC Application Note 5.53 dBm

(66)

7.4 Measurement of the LNA Prototype 1 dB Compression Point 47

(67)

7.5 System Measurements

The next step in the verification process is to make complete system measurements with the LNA prototype connected with the Hammerhead A-GPS chip, and make comparisons with the previously used LNA, BGA615L7E6327, a Silicon Germa-nium GPS Low-Noise Amplifier from Infineon. System measurements where done with the LNA prototype which had the OMN change operating at ID 9.7 mA.

These results can be seen in table 7.10. The measurements are taken after the mixer in the intermediate frequency (IF) band (2 MHz).

Some more information about the content of table 7.10 are presented shortly as follows:

System Gain Measured with the PGC, Programmable Gain Con-troller, disabled. Typically the PGC compensates so that the system gain is around 126 dB, with the PGC disabled the gain of external LNA can be seen by comparing the internal gain with the system gain.

System NF Noise measurement using a derivative from the Y-factor technique (appendix C). The major difference is that the technique in appendix C calculates gain first, that can be included in the cascaded noise from the measurement instrument.

w/ NM NoiseMaker, baseband noise is added with the signal.

BB Noise measurement using baseband as signal input, as opposed to using a noise source which the Y-factor does. This measurement is based on a Signal to Noise Ratio (SNR) measurement, where an external LNA is added, which has a known gain and noise. For a more detailed description, please see appendix D. SSm -1nn dBm Signal Strength Measurement at two different power

levels. -140 dBm is an "open sky" scenario where the integration time is lower than in the -155 dBm mode which simulates a scenario with weak signal levels. In -155 dBm mode the integration time is increased (effectively meaning the bandwidth is low-ered) to lower the noise floor (see (3.5)). The value displayed is when the signal to noise ratio (SNR) is 10.

(68)

7.5 System Measurements 49 T able 7.10. System Measure m en ts. External LNA System Gain System NF System NF System NF S Sm -140 S Sm -155 (dB) (dB) w/ NM (dB) BB (dB) dBm (dBm) dBm (dBm) NEC 94.28 1.25 1.34 1.15 -147.25 -160.73 BGA615 93.42 1.49 1.53 1.35 -147.36 -160.71 None 79.50 4.08 – – – – With SA W filter enabled NEC 93.67 2.05 2.15 1.72 -146.66 -159.40 BGA615 92.92 2.25 2.30 2.05 -146.44 -159.15

(69)

50 Measurement Results Differences in Noise Measurements

There is a difference between the noise measurements results depending on which method is used. Both are represented in the comparison tables in section 7.5.1 to give the reader a sense of which span the noise has, depending on method of measurement. Typically the noise result calculated from the method using the baseband is on an average 0.17 dB lower ranging from 0.06 dB to 0.33 dB. The source of the error is most likely due to the ambient temperature of the noise source is not 290 K, but rather 295 K.

(70)

7.5 System Measurements 51

7.5.1 Comments on Results Displayed in Table 7.10

Using the gain and noise figures from table 7.8 when the NEC LNA is working in 9.7 mA and combining them with the cascaded noise figure (2.1) the results can be compared to the gain and noise in table 7.10 and are presented in table 7.11 and 7.12.

Table 7.11. Calculation cascaded gain and noise of individual measurements and

com-parison against full measured system.

Measured Gain (dB) Noise Figure (dB)

NEC LNA 15.54 0.80

Balun -1.0 1.0

Internal LNA 79.50 4.08

Cascaded Calculated 94.04 1.02

Results table 7.10 94.28 1.17 . . . 1.25

Table 7.12. Calculation cascaded gain and noise of individual measurements and

com-parison against full measured system with SAW filter enabled.

Measured SAW enabled Gain (dB) Noise Figure (dB)

NEC LNA 15.35 1.50

Balun -1.0 1.0

Internal LNA 79.50 4.08

Cascaded Calculated 93.85 1.70

Results table 7.10 93.67 1.72 . . . 2.05

Table 7.13 shows how the system noise figure is dependent on the receiver sensitivity. When measuring without SAW filter both LNA:s have a minimum detectable signal level at -160.7 dBm. There seems to be a limitation in the HammerHead-I chip at these power levels, since the 0.2 dB difference in noise should result in the same difference in signal level. This relationship is seen in (3.5). When the SAW filter is enabled the signal levels will drop due to the losses