# Radio frequency communication

# Radio frequency communication

### 1.0 Introduction

In radio frequency communication, it will be important to amplify very weak signal and as well tend to reduce the noise level and losses on the feed line to a level that is detectable by the receiver. When we amplify the signal, noise increase as well but these losses/noise are acceptable and effort made to limit the losses. Low Noise Amplifiers (LNA) is very important component in the link budget or rather block diagram of a RF communication. LNA is usually the primary component of the low noise block (LNB) cascade at the receiver end of a satellite communication.LNA has a specific achievable gain, noise figure and intermodulation (3rd order intercept point).The aim for making it the first component in the cascade of LNB are; to set the noise floor for the entire cascade at relatively low dB and a maximum gain that greatly reduces the noise figure contributions of the rest of the components in the cascade. A GaAs MESFET - Gallium Arsenide Metal Field Effect Transistor is made of gallium arsenide semiconductor substance and Schottky junction used for the conducting path. 2.4GHz - GaAs MESFET has a good uniformity, threshold voltage control and low cost makes it fundamental for front end microwave IC applications design.

LNA ensure that the noise introduced by the LNB during the frequency conversion and amplification processes is very small hence the name low noise. This can be viewed to ensure that the degradation of the signal to noise ratio in decibels with the LNB is small. And ensure the LNB doesn't greatly amplify the inter modulation components to levels that may degrade the desired signal. The degradation which arise from physical obstruction to the line of sight such as interferences from building,refraction,reflection,diffraction,path loss, temperature noise and ionisation from the environment. For the low noise to be achieved on the line the amplifier should have high amplification in the first stage of the cascade. The choice of transistor which is usually represented by scattering parameter is important to attain the required gain and noise figure for the design. Since MESFET energy efficiency is low or not but lessen the comparative quantity of noise available. Then biasing is done to prevent leaking of signal away from the signal path.

### 2.0 Background Review

In the design process of a Low Noise Amplifier it was essential to have basic understanding of the background concept and principles. These include transmission line, reflection, scattering parameters, smith chart, impedance matching and transformation.

### 2.1 Transmission line and parameters

As an essential component in recent wireless systems transmission lines are used for amplifiers and mixers impedance matching then connecting antenna transmitters to receivers. The main objective of a transmission line is to shift a signal from a source through certain distance to a remote load. This is shown in figure (2.1) below. Inductors, resistors and capacitors are used in building and implementing impedance matching networks. As the frequency in a network increases and becomes too large the inductors, capacitors and resistors value will be impractical leading to parasitic values. The transmission lines will be used in place of these inductors, capacitors and resistors on the line to overcome the problems introduced by these parasitic issues. The main dissimilarity between a transmission line and standard electrical circuit being on the electrical dimension. In circuit analysis the physical sizes of the network are assumed to be smaller than the electrical wavelength but transmission lines are seen as significant fraction of many wavelengths or wavelength in size. We can then say a transmission line is treated as distributed parameter networks which involve currents and voltages varying in magnitude and phase over its length of line.

The transmission lines would be in form of a coaxial cable, micro strip, strip line or twisted wires because they can be modelled as Lumped element circuits which are made up of R, G, L and C denoting series resistance measured in Ohm/metre, shunt conductance measured in S/metre, series inductance measured in Henry/meter and shunt capacitance measured in Farad/metre per unit length respectively of the transmission line.(Pozar,2001). Whereas R and G show the loss along the line.

In transmission line problem and calculation interests lie mostly on the electrical length than physical length. The electrical length shows the precise multiple or fraction of a wavelength at a given frequency which is typically expressed as an angle. Consequently, the whole wavelength represents 360 degrees (2π radian). It is good to show that the physical length is related to electrical length by propagation velocity. Showing the wavelength as a 360 degrees, a phase constant β = measured in radian per metre. And say given a real physical distance,l, the product of the distance covered and phase constant is βl which represents the total electrical length, in radians.

### 2.2 Reflection

When considering impedance seen by the generator on applying a pulse. It takes a limitedtime for the pulse to move down the line to the load and the generator cannot see the impedance at load rather the impedance seen by the generator is characteristic impedance of the cable itself which is usually 50 Ω or 75 Ω. Since voltage exists at the termination or load then a current must be flowing and power must be dissipated in the load for the period the pulse. The cable has some attenuation (loss) but comparatively small proportion of the voltage entering the cable is dropped. This is conceivably the main reasonto value about transmission lines. Even though the characteristic impedance Zo is a real part, the power entering the line is not absorbed by the line itself rather it is transferred to the load at termination. Inductors and capacitors are the largely available reactive elements on the line and they (L and C) do not dissipate energy instead they transfer it. [RGC,2008].So reflection occurs when the load/termination impedance has a different value for a particular combination of voltage and current. There is an impedance discontinuity at the travelling power wave which will result in a fraction of the wave being reflected. This will cause the incident wave to lose some of its magnitude which is undesirable trend in most communication application where power management is crucial. The degree of incident power loss is associated to the match of impedances seen at the source and termination. So it aims at optimizing the impedance matches in order to maximize the power transfer which is very important in a transmission line. The impedance network matching has many parameters that characterize their performances.

Reflection Coefficient (Γ) defined as “the ratio of the reflected wave to the incident wave which can be expressed as impedances describing both magnitude and phase shift” which can be represented as below.

From Figure (2.2) showing the measurements and impedance used in solving reflection coefficient. This is the load reflection coefficient (ΓL) with respect to the generator impedance. Conversely it is the ratio of load impedance minus source impedance to load impedance plus source impedance. When the load is terminated in a short (short circuit) the negative reflection is maximum therefore the reflection coefficient is -1. But when the load is an open circuit the positive maximum reflection occurs and the reflection coefficient is 1. In an ideal transmission line where the Zs = Zl (source impedance is equal to load impedance) we can say that the line is perfectly matched and there is no reflection and the reflection coefficient is zero.

Another very important parameter in transmission line application is the Voltage Standing Wave Ratio (VSWR). The addition of incident and reflected wave travelling in the opposite direction would give rise to standing waves which is defined as “the ratio of the maximum voltage to the neighbouring minimum voltage of that standing wave”.As shown in equation (2.2). In an ideal transmission line that is a perfect matched condition where there is no reflection, VSWR takes an ideal situation and minimum value. . [Edwall,2008].

### 2.3 Scattering Parameters

The S - parameters and scattering parameter describe the typical behaviour of radio frequency component in a network which is usually expressed in matrix. They are complex numbers (they have both magnitude and phase) which state the behaviour of propagation of voltage waves in radio frequency region. This is basic because it interpret and represent radio frequency networks as a single device [Edwall,2008].

The scattering parameter matrix for a (N=2 - port see figure 2.3) that is 2-port network is given by

Where;

S11 - the forward/input reflection coefficient

S21 - the forward transmission coefficient

S12 - the reverse transmission coefficient and

S22 - the reverse/output reflection coefficient

Scattering parameters are important in microwave communication because they can be measured for both matched and mismatched networks.S-parameters simplify the amplifier design applications describing information on the stability and gain of the transistor.

### 2.4 Smith Chart

Smith chart is an important design tool for RF engineering though it has been involved in computer aided design software but still very useful. It is necessary to understand the principles on which smith chart works because it helps you visualize what happens in a transmission line applications. The smith chart is basically made up the reactance and resistance circles. It provides standard for reflectance, gain circles, stability circles, graphical presentation etc. It can be regarded as plot of reflection coefficient on complex plane. In smith chart; the reflection coefficient is plotted on the Cartesian coordination of the circle. The radius of the smith chart is taken to be unity or one therefore plotted values either admittances or resistances must be normalized regarding to a reference given by equation (2.41 and 2.42 resistances and admittances respectively);

The reference point in question is usually the characteristic impedance (Zo) of the network which is taken to be 50 ohms.

### 2.6 Impedance Matching/Transformation

Impedance matching is required to maximise power transfer from generator/source to load. Maximum power is transferred to the load when a network is properly matched since a matched network reduces reflection and provides low VSWR. Since Maximum power theorem aim at reactive components cancelling each other, the objective is that Zlmatches Z2 and Zs matches Z1 or Z1 matches Z2 respectively.

In microwave engineering matching is achieved with transmission line representation or Lumped element. But transmission line matching is preferable to Lumped element matching because at high frequencies the inductors, capacitors inherent in lumped element are not desirable due to lossy and parasitic nature at those frequencies. These issues make it difficult to get the exact values of the lumped elements. Transmission line matching is free of this. Consider figure (2.6) where there is transmission line 1 and 2 with their respective characteristic impedances Zoa and Zob. If we assume Z1 is not equal to Z2 and that line 1 is connected directly to line2.The existing power in line 1 will not be transfer to line 2 rather dissipated on the line due to reflection. The matching network therefore removes the mismatch situation when placed between line 1 and line 2 to transform Zoa to Zob.

There are various matching techniques using transmission lines that are outlined in [Pozar,2001] and listed below:-

- Quarter wave matching
- Open circuit (Series and Shunt) stub
- Short circuit (Series and Shunt) stub
- Broadband matching
- Double stub matching

The quarter wave impedance matching technique which is mostly used for this design process is simply determining the characteristic impedance Zo by setting the length of the transmission line fixed at quarter the wavelength which is obtained by the following equation;

When the characteristic input impedance and characteristic load impedance are real part or value it makes the mathematics easier. But in case of complex part (imaginary part) involved in one of the above which require one of the reactance parts of the impedance to be matched have to be cancelled. The quarter wave matching would be achieved by adding extra shunt or series reactance to the matching network. This makes quarter wave impedance matching simpler to use.

### 2.6.1 Microstrip

Microstrip consists of a dielectric (substrate) of which one surface is used as signal paths for electromagnetic waves and the other used for conducting ground plane. The ground and signal planes may be made of any suitable conducting material such as copper with an even thickness. The microstrip is a planar transmission implementation used in RF circuits. This is because at high frequencies the lumped elements inductors and capacitors tend to be very small values and difficult to realise in its applications.Microstrip offers a simpler geometry in solving the above problems and cheap and easier to fabricate. Microstrip would be use for the design process and fabrication. The characteristic impedance of any strip is a function of the strip width and length (or generally the area) if all other parameters of the microstrip are left constant. From the microstrip geometry an effective wavelength λeff will results in related effective dielectric constant εeff .

### 3.0 Amplifier Design

In electronic engineering amplifiers are in form of transistors which are used to amplify small input voltages to higher output voltages. The design process is aimed at controlling the device scattering parameters. The objective is to conjugately match the input and output of the transistor to achieve a maximum power transfer required from the generator/source to load say Γl = Γout* and Γs = Γin* as shown in figure (3.0) below;

### 3.1.1 Gain

The gain of any working device is defined as the ability to amplify the voltage or power of an input signal. The power gain is then defined as the ratio of the power that is delivered by the source/generator to the power delivered to the load. It is usually defined in decibels and can be derived from the following equation(3.1)

The power gain are very essential in determining the efficiency and performance of an amplify.There are other specific definition and type of gain available which would be described below and equations for deriving them.

Operating power gain, GP

Available power gain, GA this is possible when the input and output components are conjugately matched that is Gp =GT which can be represented by equation 3,1c

### 3.1.2 Stability

An amplifier could be potentially unstable or unconditionally stable before matching technique is used to verify the stability. There is an undesirable response from the transistor leading to unwanted oscillations when the source and load terminations cause the impedances of the input and output components to have a negative real part that is any network is liable to oscillate where the real part is a negative. The instability is avoided by placing the reflection coefficient of the load and that of the source in a stable region on the smith chart [Edwall,2008]. The unconditionally stable (K > 1 and ∆ < 1 or K > 1 and B1 < 1 ) [Yip,1990] is determined by a factor K which is know as the Rollet's stability criterion derived by;

If a transistor is unconditionally stable it is easier for design process and a straight process is used. But different design approach is used for a conditional stable transistor. The reflection coefficient of load Γl is used when the Gain of the amplifier is of important while Γs is chosen when the noise figure is the primary target. It can be seen from figure 3.0 that;

Then if the reflection coefficient of the source is desired ΓL = ΓOUT* while if the reflection coefficient of the load is desired ΓS = ΓIN* where ΓIN and ΓOUT can be S11 and S22 respectively. It should be ensured that in design process at certain frequencies outside the operating frequency the out of band component is stable rather than unstable. Since noise can cause undesired effects on this amplifiers when unstable at certain frequencies. At this stage the characteristic of a transistor could be unilateral or bilateral in nature.

### 3.1.3 Unilateral and Bilateral Operation

Unilateral Operation: If at the possible operating frequency of a transistor,the value of S12 is insignificant say [S12 ≈ 0].The transistor is said to be Unilateral. In unilateral state S11 and S22 is directly matched. This helps in the amplifier design since is ΓIN = S11 and ΓOUT = S22 and the transistor is unilateral. A conjugate matching is implored at the input and output by making ΓS *= S11 and ΓL* = S22 .

Bilateral Operation:If at the working frequency of a transistor the value of S12 is significant that is equivalent or greater or close to one. The transistor is said to be bilateral. Simultaneous conjugate matching is used to achieve the value of ΓIN = ΓSm and ΓOUT = ΓLm using the following equations. Note that ΓSm and ΓLm are Gamma-source matched and Gamma-load matched respectively.

After that conjugate match the network by making ΓS = ΓSm* and ΓL = ΓLm*

Note that when the transistor is unconditionally stable simultaneous conjugate is used to solve the design process while if it is conditional stable or potential unstable no need for simultaneous conjugate matching. Remember that in simultaneous conjugate matching 2-port network is used and have S-parameters. So the value of S12 from the transistor sends a feedback response to the transmission line along Port 1[input] and Port 2[output] thereby causing instability. So we can solve it by conjugate matching.

### 3.1.4 Design based on Maximum gain

Assume there are no losses; designing for maximum gain is rooted on the fact that maximum power is delivered to the load from the available maximum power at the source when transmission lines are conjugately matched. Recall from figure 3.0 , equations (3.1j - 3.1n)above and this is given by ;

### 3.1.5Design based on Specific gain

When solving or looking for a flat response on the amplifier design to determine a specific gain as we can see in figure3.0 above. The transistor which is unmatched has a constant overall gain and it is possible by manoeuvring the matching networks. The Available gain technique provides circles of constant available gains which are plotted on the smith chart to find the reflection coefficient at the source, will provide the desired gain. However the value of will be used to calculate the reflection coefficient at the output by using the (3.1.4b). The conjugate matching is thereby performed at the load or output port by equation (3.1j).

### 3.1.6 Single Stage Amplifiers Design Exercise operating at 10GHz

The design approach for a single stage amplifier operating at a high frequency is based on working on the device scattering parameters. We usually assume the transistors to be unilateral (that is S12 = 0) which simplifies the design process. But recently with the aid of CAD tools like Microwave Office which solves and provide accurate calculations for the unilateral or bilateral nature of transistors without any assumption. This provides

more accurate results for design process. The desired characteristics like maximum gain, specific gain, VSWR etc which has been discussed above help in achieving the design.

For the preliminary design exercise using the following;

- A single stage amplifier to operate at 10 GHz using MESFET -NEC 76038
- Maximum gain possible at 10 GHz
- 50 Ohm source and load environment
- Use of Transmission line Quarter wave impedance matching to achieve matching networks

From the available device (transistor NEC-76038) data sheet. The S parameters for the device at 10 GHz with bias conditions of VDS = 3V, IDS =10mA are:

S11 = 0.57 ∟ 175°

S21 = 2.21 ∟ 27°

S12 = 0.110 ∟ 7°

S22 = 0.30 ∟-118°

The NEC- N76038A device is bilateral at 10 GHz. And the Stability factor, K was calculated with Microwave Office to be 1.228 at 10 GHz as shown in fig 3.2 below.

The device is unconditional stable at 10GHz since the value of K >1 and B1 > 1, therefore simultaneous conjugate matching would be applied to achieve the required match. From figure 3.3 the maximum possible gain is 10.15 dB and the maximum unilateral gain calculated using the Matlab code in Appendix 1 is 9.00 dB. Figure 3.3 also show the Available gain, Maximum Stable gain etc.

### .3.1.7 Single Stage Amplifiers Design Exercise operating at 2.4GHz

The NEC- N76038A device is Unilateral at 2.4 GHz. And the Stability factor, K was calculated with Microwave Office to be 0.3347 at 2.4 GHz as shown in fig 3.4 below.

The device is potentially unstable at 2.4GHz since the value of K <1 and B1 > 1, therefore simultaneous conjugate matching would not be applied to achieve the required match. From figure 3.5 the maximum possible gain is 18.32 dB

### 3.1.8 Unilateral figure of merit

There is an error when assume a transistor as exhibiting unilateral operation. The unilateral figure of merit, U helps in determining this error for the assumption. Unilateral figure of merit was described by [Pozar, 2005] as follows;

The value of U, Unilateral figure of merit is calculated using math lab. See appendix 1 for more calculations is the then substituted in equation 3.1.8b below;

The outcome of the error is high since the maximum is about 1.1773 dB that is ( 0.6086 + 0.5687). This is for the single stage amplifier at 10GHz.

### 3.1.9 Input/Output Matching Networks

The ideal transmission lines and quarter wave matching technique was used to simulate the network in microwave Office as shown in final circuit in figure 3.6, 3.7 and 3.8; First, recall that smith chart rotates by a factor of 2βl and matching is achieved by varying the phase shift of reflection coefficients at source and load (Гs and Гl respectively) to the real axis on the smith chart. Assume Zo to be 50 Ω, the electrical length (EL) required for the phase shift on the smith chart can be calculated. Remember as discussed in section 3.1.6 that at 10GHz the transistor is unconditional stable and bilateral in behaviour and need to be conjugate matched. From appendix 1 (matlab simulations), values of Гs and Гlwere { 0.7475 ∟ 172.2152° and 0.6084∟ -127.3151° respectively}.

Recall equation 2.1 ,

Z = from Г = (3.1.9a)

Гs = 0.7475 ∟ 172.2152° from mat lab simulation showing the magnitude and angle.

Taking the conjugate of the angle which is basically reversing the sign = ∟- 172.2152° .

EL = = 176.1° (3.1.9b)

For the magnitude = 0.7475,

Solving for Z = from equation (3.1.9a).

= = 0.144492

De normalising it (0.144492 * 50) = 7.225

Finding Zo = = = 19.006

Summary for Reflection coefficient at the source after simultaneous conjugate matching was ;

Zo = 19.006Ω

EL = 176.1°

Secondly for the Гl = 0.6084 ∟ -127.3151° from mat lab simulation showing the magnitude and angle.

Taking the conjugate of the angle which is basically reversing the sign = ∟127.3151° .

EL = = 26.34° (3.1.9c)

For the magnitude = 0.6084,

Solving for Z = from equation (3.1.9a).

= = 0.2435

De normalising it (0.2435 * 50) = 12.1736

Finding Zo = = = 24.67

Summary for Reflection coefficient at the source after simultaneous conjugate matching was ;

Zo = 24.67Ω

EL = 26.34°

### 3.1.10 Microstrip implementation

Implement the design cicuit using the Microstrip transmission lines for the Duroid 5880 Circuit Board that is replacing the ideal transmission line with microstrip.It is suitable to describe physical transmissions lines as dimensions rather tehn electrical characteristics which ever microwave office provides that. The Electrical length,frequency,characteristic impedance of the ideal transmission line will be replaced by Length and Width of Microstrip lines. Consider that 50 Ohm feed lines will be required at the input and output ports which is approximately 15mm long, then an ideal physical ltransimision line on the circuit though it has no effect on the circiut but for layout purpose when finally building the circuit on RT Duroid board.[Clarke, 2009]. See figure 4.0 for the schematic representation on microstrip transmission line.

- Circuit Board = Duroid 5880
- material = Copper
- Dielectric constant = 2.2
- Height = 787µm
- Conductivity =58.8µm
- Thickness = 17.5 µm

At the course of design using microstrip at operating frequency of 10GHz, it was observed that the length is comparatively short and at some point when compared with the width of the line. This caused a slight deviation from the matched transmission lines as can be seen in figure 4.1 and 4.2 respectively at 10GHz.Then optimization was used to correct this shift as shown in figure 4.3 and 4.4 respectively.

### 3.1.11 Layout

The design layout of the transmission line(on Microstrip) as would be on the RT Duroid board with gap for the MESFET transistor in between the two transmission line as shown in figure 4.5 and figure 4.6 below .

### 4.0 Noise and Noise Figure

Noise arises from excitation of electrons in a conductor due to heating and it occurs in almost all electronic devices. In any design it is to know the level of noise and how noise builds up. “Noise limits the system sensitivity and be taken into consideration when designing a RF systems”[Ranson,2004].

However in noise definitions, Noise Factor nf which is a ratio of output to input signal to noise ratios while NF is the noise figure which is the dB value of the noise factor (see equation 4.0). The noise factor is usually the elementary noise performance parameter. However noise factor can be seen as the measure of the degree at which low noise amplifier degrades the SNR (ratio of signal power to noise power - equation 4.1). From the above then noise factor nf must be greater than one so that NF will be greater than zero. In principle all noise is considered to be at the input with ideal amplifier at the output [Ranson,2004].In amplifier cascade network, noise temperature plays an important part especially when the noise figure is exceptionally low. Noise temperature is usually referenced at 290K [Edwall,2008].

### 4.1 Sources of Noise in Amplifiers

Noise in amplifier systems can be viewed differently as noise received at the input and the noise generated in system by the amplifier. Noise is usually at the input of the cascade. The sources of noise can be thermal, shot noise, ionisation noise or flicker noise etc. {“Thermal or Johnson Noise: Electrical noise arising from agitation of electrons in a conductor due to heats. Shot Noise: Noise caused by current fluctuations arising from discrete nature of electron movement. Avalanche or Ionisation Noise:Current fluctuations due to reverse breakdown in semiconductor junctions. Flicker: Occurs in almost all electronic devices and is associated with crystal surface defects”}[Ranson,2004].

### 5.0 Conclusion & Recommendation for main project

This pilot study work has exposed me to necessary background information, microwave designs fundamental principles and understand actual procedures rather steps for designing a Low Noise Amplifier. The use of Microwave office CAD tools for matching networks, amplifier gain, noise figures and stability etc. The design exercise preliminary above posed difficulties especially when trying simultaneous conjugate matching networks for the unconditional stable amplifier. In theory transmission lines behave ideally but deviates actually during actual design and mostly when translating them to microstrip transmission lines.

The main project will perform the actual design and fabrication of Low Noise Amplifier operating frequency at 2.4GHz as specified. Here lots of considerations are involved such as gain, low noise performance (noise figures, noise circles), stability ( at different frequencies and not just at 2.4GHz so that the circuit can be marketable),biasing the network , fabrication on Duroid board and testing. Low Noise Amplifier design have been flourishing in recent times like in satellite communications etc and the design will pose a problem but it is feasible.