1 Sensitivity System sensitivity is defined as the available input signal level S i for a given (SNR) O S i is called the minimum detectable signal.

1

Sensitivity

System sensitivity is defined as the available input signal level Si for a given (SNR)O

Si is called the minimum detectable signal An expression for Si can be derived from

the noise factor definition as follows

Recall that from the previous lecture Ni=kTB for maximum delivered power

o

o

i

i

S

N

N

SF

o

oii N

SFNS

o

oi N

SkTBFS )(

2

Sensitivity example

What minimum input signal will give an output signal to noise ratio of 0 dB in a system has an input impedance of 50 Ω, a noise figure of 8 dB and a bandwidth of 2.1 kHz, T=290º K?

Solution:We can use the previous equation to find Si

o

oi N

SkTBFS )(

o

oi N

SkTBFS log10)log(10)log(10)log(10

3

Sensitivity example

0)10/101.22901037.1log(108)log(10 3323 iS

dBmSi 133

• Alternatively Si as a ratio can be written as

• Note that Si is related to the input voltage according to

• The input signal voltage is then found to be

WSi4102.5 1

4

Sensitivity example

What is the minimum detectable signal or noise floor of the system in the previous example for an output signal to noise ratio of 10 dB

Solution:If we follow the same procedures as in the

previous example then we have

This shows that a larger input voltage is needed at the input of the receiver to raise the SNRO to 10 dB

5

Sensitivity example

Consider a communications receiver with a 50 Ω input impedance, a B of 3 kHz, and a 4-dB noise figure. What will be the minimum detectable voltage level

Solution:The noise floor of this receiver for an

output signal to noise ratio of 10 dB is found to be

6

Sensitivity for antenna and receiver

If an antenna is considered with the receive, then the total output noise is

Where Fa is the antenna noise factor, Fr is the receiver noise factor , Ni is the available noise from the input and Na is the noises added by the receiver

The output signal to noise ratio is

7

Sensitivity for antenna and receiver example

A given receiver system composed from an antenna with a noise factor of Fa=100, What will be the minimum detectable signal level if the receiver noise factor is =2.5 and the SNRO of the system is 10 dB. Assume the temperature is 290º k and the system band width is 3 kHz

dSolution: The input signal is given by the equation

kTBFFN

SS rai )1(

8

Sensitivity for antenna and receiver example

Solution:

14323 1029.11031037.1)101100(10 iS

VRSE gii6106.14

9

Intermodulation distortion

All communication Rx contains some degree of non linearity

This non linearity can affect either1. the frequency of input signal2. Change the overall network gain

The network non linearity can be described by the power series expansion

y(x) is the network output and f(x) is the network input

10

Intermodulation distortion

If f(x) is given by

Then y can be written as

If y is expanded then an expression similar to the shown in the next slide will be obtained

11

Intermodulation distortion

12

Intermodulation distortion

The frequency spectrum corresponds to the previous equation is illustrated below

13

Gain compression

One effect of the non linearity is that the amplitude of the signal became

Normally K3 will be negative and large A2cosω2t will mask the smaller A1cosω1t

This reduces the gain because of the third-order coefficient K3

Multiple signals will result in a further reduction of the gain

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3314

33111 AAAkAkA

t1cos

14

Gain compression

The ratio of the gain with distortion to the idealized (linear) gain is

This is referred to as single-tone gain compression factor

An important point to mention here is the 1-dB compression point which is defined in the next slide

15

1-dB compression point

The 1-dB point is defined as the point at which the power gain is down 1 dB from the ideal

Receivers must be operated below their gain compression if nonlinear region is to be avoided

16

Second harmonic distortion

Second harmonics will occur at the receiver because of the K2 term

The amplitude of the second harmonic will be

17

Intermodulation distortion ratio

The intermodulation is caused by the cubic term of y

The cubic term will create intermodulation frequencies and

if ω1 and ω2 are of approximately the same frequency, then

The terms and will be filtered out

The terms and can not be filtered out and will appear in the output as distortion

212 122

212 122

212 122

18

Intermodulation distortion ratio

The intermodulation ratio (IMR) is defined as the ratio of the amplitude of one intermodulation terms to the amplitude of the desired output signal

19

Intercept point

The intermodulation distortion (IMD) power is defined as

If the two input amplitudes are the same, then the distortion power varies as the cube of the input power

This means for every 1-dB change in input power there is a 3-dB change in the power of the intermodulation terms, in this case 3idd PkP

20

Intercept point

Where the power in one signal component and kd is the scale factor

The intermodulation ratio can then be defined as

Where Pd is the intermodulation power and Po is the desired output power

21

Intercept point

A normalized plot of the desired output and intermodulation powers is shown blow

Power transfer characteristics, including the third–order intermodulation distortion Pd and the two tone third order intercept Pi

22

Intercept point

The intercept point is defined as the value of the input power for which the IMD power is equal to the output power contributed by the linear term

At the intercept point

A receiver’s intercept point is a measure of the distortion in the receiver

It is also a measure of the Rx ability to reject large-amplitude signals lie in close frequency proximity to a weak signal targeted for reception

23

Intercept point example

Example: If a given system has an intercept point of +20 dBm, What is the IMR for an input signal power of dBm?

Solution: 2

I

iIMR P

PP

dBPIMR 4020202

IiI

iIMR PP

P

PP 1010

2

10 log102log102log10

24

Dynamic range

The dynamic range is defined as the minimum detectable signal to the signal power that causes the distortion power to be equal o the noise floor Nf

Note that the noise floor is defined as Nf=KTB

Recall that the ideal power is given by

Also the intermodulation distortion ratio can is

25

Dynamic range

If the distortion referred to the input is defined as then

When Pdi is equal to the noise floor Nf,

Therefore the dynamic range DR is

OR

26

Dynamic range example

Example: A given receiver has an intercept point of 20 dBm. What will be the dynamic range for an output signal to noise ratio of 10 dB if the noise figure of the receiver is 8 dB and the bandwidth is 2.1 kHz?

Solution:The minimum detectable signal can be

found from0(S/N)*FKTBSi

oi SNRBKTNFS 101010 log10)(log10)(log10

27

Dynamic range example

The Dynamic range is given by

dBmS

S

i

i

123

10)101/101.22901037.1log(108)log(10 3323

dBDR

SIPIDR

3.95)12320(67.0

)log(10)log(10*)3/2(