International Africa University Faculty of Engineering Eight Semester Course Title: Telecommunication 2 الإتصالات2 Code: EE422 Credit Hours: 3 Lecture (2) Transmission lines Instructor: Eng. Mohammed Salih 2015 - 2016

Fig 3. Cascades noisy networks The usefulness of noise figures is demonstrated by considering the cascaded networks of fig.3. Fig 3. Cascades noisy networks using the definition of Eqn (7) in the previous lecture , we can write the overall noise figure for the cascaded network as

We assume that the networks are matched, i We assume that the networks are matched, i.e the output resistance of the first network is equal to the input resistance of the second network, and that the input noise Ni is the noise produced by a matched source at 290 k. the noise figure of the first network is therefore

In defining the noise figure of the second network the input power is also Ni hence. Thus the overall noise figure may be written But Therefore (8)

Equation (8) can be expanded to include any number of cascaded networks. The equation for three networks in cascade is (9) The effective noise temperature of a network is an alternative method of describing the noise performance of a network, this alternative is especially useful when considering low – noise networks or network in which the input noise is not produced by a matched source at 290 k. .

The effective noise temperature of network is determined by replacing the noisy network by a noise free network with an equivalent noise source at its input The temperature of equivalent noise source is chosen to make the noise at the output of the noise free network equal to the noise at the output of the noisy network. Referring to fig 2, the noise produced by the network is replaced by an equivalent noise source of the factor is the noise delivered by an equivalent matched source at temperature Te.

The temperature Te is known as the effective noise temperature of the network. If the value of Te«290K the network itself contributes very little extra noise. The relationship between noise figure and effective noise temperature is Ts is the standard temperature equal to 290K. Hence (10)

It is often convenient to represent cascaded networks in terms of effective noise temperature , substituting Eqn (10) into Eqn (9) gives (11) This equation is particularly useful when considering the noise performance of a cascaded system in which the first element is an antenna with an effective noise temperature not equal to 290K.

The insertion loss of a passive network is the reciprocal of power gain (12) When a passive network is matched at both the input and output the insertion loss has the same numerical value as the network noise figure, i.e. F=L. Both F and L are usually measured in decibels.

Example 1 The receiver which has a video bandwidth of 5.5MHz, is coupled via 70Ω coaxial cable with an insertion loss of 6dB to an antenna with an effective noise temperature of Ta=290K. The noise figure of the receiver, referred to a matched source of 70Ω at 290K is 6dB. Find the SNR at the receiver output when the open circuit signal voltage at the antenna terminals is 1mv rms.

solution Each component in this system will cause a degradation of the SNR. The maximum value of SNR will occur at the input to coaxial feeder. We begin by determining the SNR at this point and to do this we consider the antenna as both a matched signal and noise source as shown below. Matched antenna

Since the antenna open-circuit signal voltage is 1mV rms the voltage across the 70Ω load will be half this value i.e 0.5mV rms. The signal power delivered to coaxial feeder will be The noise power delivered by the antenna which acts as matched noise source, is Np=k∆fnTa. The SNR at the feeder input is thus The overall noise figure is

F1 is the noise figure of the feeder=L=6dB, i.e F1=3.98. Ap1 is the reciprocal of the feeder insertion loss and has a value of 0.251. F2 is the received noise figure =6dB=3.98. Hence the overall noise figure is F=15.85 (12dB). The SNR at the receiver output will then be

Example 2 Electrical resistance R at Temperature T is connected to electric circuit with internal resistance Rin find: Expression of input noise power to the circuit according to the Rin. Value of Rin that gives the maximum noise power. Draw approximately the Ni verse Rin

Example 3 A linear system is composed of 3 stages matched to each other as shown in the figure below. Calculate the overall noise figure and also its equivalent noise temperature.

Voltage and Current Relationship on the Line

Parameters used to describe transmission line

Note that in this equations, the impedance terms have been multiplied by the length of the element,

Line Parameters

Characteristic Impedance

Reflection from the Load When we say the line is matched we mean that the forward wave is totally absorbed by the load, consequently there is no reflected wave and V2 is zero.

Assignment (1) 1- Find the equivalent thermal Thevenins for the circuit below between point a, b.

2- For the circuit in the figure below, find: Signal to noise ratio at the input. Signal to noise ratio at the output. Noise figure F.