Noise FigureSignal - to - noise ratio : The ratio of desired signal power to undesired noise power . Noise Figure : a measure of the signal - to - noise ratio between input and output of the component . Noise Figure F

: input signal power: input noise power: output signal power: output noise power

where =290KConsider the following noise network

G : gain the network B: bandwidth

: equivalent noise temperature

Noise Figure is defined for a matched input source and for a noise source that consists of a resistor at temperature =290K .

Noise figure and noise temperature are interchangable .Consider the following loss line or attenuator with loss L and temperature T . Since the entire system is in thermal equivalent

is the noise generated by the line and L=1/G

If the line is at temperature , F=L . This states that a 10 attenuator at room temperature has a noise figure of 10 .Noise Figure of a cascaded systemConsider the cascade of two components as shown below

: gains : noise figures

: equivalent noise temperature

The noise power at the output of the second stage is

We define the equivalent network as

Therefore , we obtain

For an arbitrary number of stages , we obtain

Example :Consider the following wireless local area network (WLAN) receiver , where the bandwidth of the bandpass filter is 100MHz centered at 2.4GHz . If the system is t room temperature .

(a) Find the noise figure of the overall system .(b) What is the resulting signal - to - noise ratio at the output , if the input power level is -90dBm ?(c) Can the components be rearranged to give a better noise figure ?Solution :The noise figure of the cascade is

If , than we get The noise power output is

Thus

The best noise figure would be achieved with the arrangement shown below

Then the noise figure is

In practice , however , the essential filter may serve to present overload of the amplifier and may not be allowed to be moved .

Low Noise AmplifierThe noise figure of a two - port amplifier can be expressed as

where : source admittance presented to transistor

: optimum source admittance that results in minimum noise figure . : minimum noise figure of transistor , attained when

: equivalent noise resistance of transistorAlso we have

The quantities , and are the characteristics of the particular transistor being used and are called the noise parameters of the device .

and

Therefore , we obtain

Constant Noise Figure CirclesFor a given noise figure , we define a noise figure parameter , called

, as

This equation can be written as

or

If we now multiply both sides by . we obtain

or

This is a family of circles with as a parameter . The circles are

centered at

with radii

When , then =0 , , and . The centers of other noise figure circles are located along the vector .Example : Noise Figure CirclesA certain GaAs MESFET has the following noise - figure parameters measured at , with a 50- resistance for a frequency of 9 GHz.

Plot the noise - figure circles for given values of at 2.5 , 3.0 , 3.5 , 4.0 , and 5.0dB.Solution :1. From values of , and for at 2.5dB are computed as follows :

2. Similarly , the values of , and for at 5dB are also computed .3. All values are tabulated in Table .Table : VALUES OF NOISE - FIGURE CIRCLES

(dB) 2.5 3 3.5 4 51.78 2 2.24 2.5 3.160.21 0.45 0.71 1 1.720.40 0.33 0.28 0.24 0.180.37 0.51 0.55 0.66 0.76

4. The noise - figure circles are plotted in the Figure .

Example :A AaAs is biased for minimum noise figure and has the following S parameters at 4GHz ( ) , , , . Since is relatively small , we assume the device is unilateral . Then design an amplifier having noise figure with the maximum gain that is compatible with this noise figure .Solution : We first compute the center and radius of the noise figure circle :

Next we calculate data for several input section constant gain circles .

1.0 0.805 0.52 0.3001.5 0.904 0.56 0.2051.7 0.946 0.58 0.15

(a)

(b) We see that the gain circle just intersects the noise figure circle and that any higher gain will result in a worse noise figure . From the Smith Chart , the optimum solution is then which yields and . For the output section , we choose for a maximum of

The transistor gain is

The overall transducer gain is

A complete AC circuit for the amplifier , using open - circuited shunt stubs in the matching sections , is shown in the figure .

Example :The scattering and noise parameters of a GaAs FET measured at three different optimum bias settings at f=6GHz are :Minimum Noise Figure ( ) :

Linear Power Output( )

dBF 9.2min

Maximum Gain ( )

Design a microwave transistor amplifier to have good ac performance .Solution : There are four ac performances that must be considered : noise figure , power gain , power output , and input and output VSWR . The linear power- output bias point ( ) provides a good compromise between the minimum noise figure and maximum gain . At this bias point , the Table gives the noise , gain , and power parameters . The output power performance , measured ant the 1-dB compression point , was experimentally measured and it is given in the figure . The data for the output power were taken with an input power drive of 8.3dBm

Noise Parameters Gain Parameters Power Parameters

05.104575.0 L09.103718.0 ML

dBF 9.2min

dBGA 33.9

The input VSWR with is 1 , and the VSWR =3.82 with . In order to calculate the VSWR , we obtained (in the next page) and

used

Trade - offs between noise figure , power gain , and VSWRLast Figure shows the noise figure , and input and output VSWR as the reflection coefficient is varied from to , along a straight line , in the Smith Chart . The table shows that a good compromise between noise figure , , and VSWR is to use and . The noise figure is increased by 0.24dB from the minimum noise , but

is increased by 1.22dB and the input VSWR is improved by 40% (i.e. , VSWR =2.28) . The ac schematic of the amplifier for the selected values of and is shown in next Figure and the microstrip board layout is also shown . The board material is Duroik ( =2.23 , h=0.031 in.) . The measured characteristics of the amplifier are shown in next

page .

Figure : (a) The ac schematic of the amplifier with =1 ; (b) microstrip layout with two different dc bias networks.

(c) (d)Figure : Measured characteristics of the amplifier : (a) gain performance ; (b) noise performance ; ( c) input - output VSWR performance ; (d) wideband gain performance .Reference : “ A 6GHz amplifier using the HFET -1101 GaAs FET “ HP Application Note 970 .

Balanced Amplifiers

Figure 4.4.5 Balanced amplifier configuration .Why use balanced ?In broadband amplifiers , the design of compensated matching networks to obtain gain flatness results in impedance mismatching that can significantly degrade the input and output VSWR . The balanced configuration can be used to improve the I/O VSWR (Return Loss) .

The I/O couplers are 3dB hybrids (usually hybrids) (i.e. hybrids) .

: reverse power loss

: forward power gain

Where a and b indicate the two amplifiers and 1 and 2 refer to the input and output ports of the balanced amplifiers .If the two amplifiers are identical , then =0 and =0 and the gain (and also ) is equal to the gain of one side amplifier .Ref . K.Kurokawa , “Design theory of balanced transistor amplifiers , “ pp . 1675-1698 . BSTJ , OCT . 1965 . BSTJ : Bell System Technical Journal .