Chapter 3

1. Chapter 3 Network noise and intermodulation distortion

2. Noise • All signals are contaminated by noise which degrades the system performance • The noisiness of a signal is measured by the signal to noise ratio S/N • The S/N is defined as • The noise is defined as any unwanted input • The noise consists of both nonrandom, periodic, and random components • Non random noise examples are power supply noise, • Nonrandom noise can be eliminated through prober circuit design • Random noise can’t be eliminated in general

3. Noise • Random noise is described in terms of its statistical properties • The most common noise form of random noise originates in the Rx is thermal noise which is generated by resistive circuit elements • Other sources of noise generated from active devices will be covered in this chapter as well • These includes flicker and shot noise

4. Thermal noise • Thermal noise is a random noise generated by the motion of the conduction electrons in a resistor as discovered by J. B. Johnson • The rms voltage of thermal noise is given by As demonstrated by H. Nyquest • for a linear network the thermal noise can be re expressed as

5. Thermal noise • Thevinin equivalent circuit of the noise • If a resistor is connected to a frequency dependent network, then the total noise at the network output due to R will be

6. Thermal Noise Where G(f) is the magnitude squared of the frequency dependent transfer function between the input and output voltages E20 can be rewritten as • The integral in the above equation is called the noise bandwidth Bn • A system can have narrow 3-db bandwidth and large noise bandwidth

7. Thermal Noise Example find the total noise power generated by the impedance of the circuit shown below Solution The impedance of the parallel RC circuit is • The real part of Z(ω) is • The total noise power is

8. Thermal noise- with more than one resistor • If a given circuit contains resistors in series, then the total noise power will be • If the resistors are connected in parallel then the total noise power will be

9. Current source representation • Note that the thermal noise was represented by a voltage source in series with a resistor (Thevinin) • According to Norton theorem, thermal noise can be represented as shown below Thevinin representation Norton representation

10. Exess noise in resistors Excess noise power has 1/f spectrum The excess noise voltage is inversely proportional to the square root of frequency Noise exhibits 1/f power spectral characteristics at low frequency often referred to pink noise Thevinin representation Norton representation 10

11. Active device noise The other sources of random noise in the network is the active device noise The active devices include diodes, BJT and FETs There are two main types of noise in the active devices flicker noise (1/f) Shot noise 11

12. Flicker noise The flicker noise is a low frequency phenomenon The noise power density follow power spectral density The value of alpha is close to unity 12

13. Shot noise The shot noise arises from the current fluctuations in the active device The noise power density is given by Where q is the electron charge, I0 is the DC current flowing in the device and k is a constant varies from device to device depending on how the devise is biased In a junction transistor k=2 13

14. Shot noise The shot noise equivalent circuit for forward biased pn junction is shown below A uniform power spectral density and the total noise current squared is proportional to the bandwidth according to If the additional 1/f noise is added then the total noise current is 14

15. Spectral density function of the total noise At frequencies below fL the noise power density increases at a rate of 6 dB per octave At frequencies much higher than fL the noise power is equal to the shot noise independent of frequency Power density of the total noise current as a function of frequency 15

16. Spectral density function of the total noise If the noise current is connected to a frequency dependent network, then the mean-square current at the output will be Power density of the total noise current as a function of frequency 16

17. Noise in transistor amplifiers From the previous discussion any amplifier generates noise Thermal noise in the bias resistors Shot and 1/f noise generated by the transistor in1 and in2 represents the shot noise current densities at the input and the output of the device (these noise currents arises from the base emitter and Collector emitter diodes) 17

18. Noise in transistor amplifiers If the transistor output impedance is much larger than RL, The output noise voltage due to in2 will be 18

19. BJT noise The principal noise sources in BJT are Input shot noise Output shot noise Thermal noise created in the base spreading resistor At high frequencies above fT of the transistor the noise currents increases according to 19

20. FET noise The FET noise source are given below Where gm is the transistor mutual conductance and Ig is the gate leakage current 20

21. MOSFET and JFET noise These two types of transistors have noise expressions similar to FET The MOSFET has a negligible gate current Ig The shot noise increase with frequency The total noise current is given by 21

22. MOSFET and JFET noise Where Cgs’ is two third the gate to source capacitance 22

23. Noise Figure, noise factor and sensitivity The SNR is the best measure of system input and output signal quality Another concept for describing how much noise is added by the circuit is used which is the noise factor The noise factor F has become a standard figure of merit of the noise added in a circuit The noise factor is defined as 23

24. Noise Factor The noise factor depends upon the noise generated in the device and on its input termination The noise factor does not depend on the device output termination 24

25. Noise Factor The output noise power is equal to Ni+Na Where Na is noise added to the device output by the device added per unit bandwidth By definition the noise factor expression became as Where Ni is the available input noise per unit bandwidth 25

26. Noise Factor With small modification to the above equation the noise factor can be redefined as The noise figure is a measure of the degradation of the signal to noise ratio due to the noise added in the system 26

27. Noise Factor Note that the maximum available power from a given source is this means that Therefore the noise figure can be rewritten as This is the noise figure measured in a unity bandwidth at a particular frequency 27

28. Noise Factor The equation is often referred to as the spot noise factor Note that in ideal receiver the noise factor is only one since no noise is being added (Na=0) 28

29. Average noise Factor The noise performance of a communication system normally needs to be described over a range of frequencies This can be done by using the average noise factor The average noise factor is given by the following equation Where G(f) is the system power gain (transducer power gin) 29

30. Noise Figure The noise figure is defined as The noise figure is more commonly used compared with the noise factor 30

31. Noise factor in cascaded system What is the overall noise factor in cascade system where more than one blocks are cascaded together? The noise factor of the cascaded system can be given by 31

32. Noise factor of cascaded networks Example: for the system shown in the figure determine the overall system noise figure Solution: The overall noise factor can be given by 32

33. Noise factor of cascaded networks Similarly The overall noise factor is 33

34. Noise temperature The noise factor will normally lie between 1 and 10 Note that If then or alternatively Where Tr is referred to as the system noise 34

35. Noise temperature example What is the variation in noise temperature as the noise factor varies from 1 to 1.6? Assume T=290º K Solution 35