1. AM Demodulation or AM Reception and AM Noise
CHAPTER 2 – Part 4
AM Demodulation or AM Reception and AM Noise

2. Introduction
The ultimate goal of any communications systems is to extract the intelligence from the transmitted signal, process it, amplify it and reproduce it faithfully into a load at the destination.
Typical loads for received AM signals are such as sound system loudspeakers and TV video screens.
Scope of this part will be how the received signal is processed, original tuned radio frequency (TRF) receiver and modern superheterodyne receiver and characteristics common to all receivers.

3. Simplified Block Diagram of an AM Receiver
Figure 33

4. Demodulation Demodulation is the reverse process of modulation.
In the receiver the frequencies are down-converted rather than up-converted (as in transmitter).
A small fraction of the transmitted modulated signal is captured by the receiving antenna.
At the receiver the information contained in it must be separated from the carrier and passed to the load.

5. Cntd…
This separation process is called demodulation or detection and involves stripping the carrier wave from the intelligence (audio signal) and amplifying the original intelligence signal to some usable level.
The circuit used for this process depend on the modulation employed in the transmission of the signal.
Example for conventional AM signal or simply AM is envelope detector or simply detector.

6. Diode Detector The simplest and most widely used AM demodulator.
The input to the circuit is the 455 kHz IF signal that has been selected and amplified by earlier RF stages in the receiver.
Referring to Figure 34: the signal is then applied to Diode, D which acts as a half-wave rectifier. An LP filter composed of the RC parallel network filters out the 455 kHz IF signal but passes the desired audio frequencies to the audio amplifier.

7. AM demodulator Circuit: Diode Detector
Figure 34

8. Waveforms of envelope detector circuit
Figure 35

9. AM demodulator: Transistor Detector
Transistors are sometimes used to provide detection and amplification in a single stage.
Transistor detectors are generally used only in low-cost, all-transistor receivers, whereas diode detectors are chosen for many kinds of equipment because of their simplicity and excellent performance.
A typical transistor detector is shown in Figure 36: Resistors R1 and R2 bias the transistor for precise class B operation, a requirement for simultaneous rectification and amplification. Resistor R3 serves as the collector load and RF components are filtered out by capacitor C2.

10. AM demodulator Circuit: Transistor Detector
Figure 36

11. AM Frequency Spectrum
The AM broadcast system covers the frequency range from 535 kHz to 1605 kHz.
It consists of 106 channels each with a BW of 10 kHz for each station’s transmitter.
Hence all AM radio receiver must capable of receiving transmitted signals at the mentioned range and must limit its BW to 10 kHz.
Also receivers must be sensitive and selective enough to select only one desired frequency from among the signals received while rejecting all others.

12. Receiver Parameters
There are several parameters commonly used to evaluate the ability of a receiver to successfully demodulate a radio signal:
Selectivity
Sensitivity
Bandwidth improvement
Dynamic range
Fidelity
Insertion Loss
Noise temperature & Equivalent noise temperature

13. Selectivity
The selectivity of the receiver is a measure of its ability to select one signal while rejecting all others at nearby frequencies.
Selectivity determines the adjacent-channel rejection of a receiver.
Selectivity is increased as the bandwidth is reduced. However the selectivity varies with the received frequency, decreasing when the received frequency increases.

14. Cntd…
One common way to describe the selectivity of a radio receiver is by giving its BW at two attenuation points i.e. –3dB and –60dB.
The ratio of these two BWs is called the shape factor and is expressed mathematically as
Ideally SF = 1. Typical AM broadcast receiver has B(-3dB) = 10 kHz and B(-60dB) = 20 kHz
SF = shape factor (unitless)
B(-60dB) = BW 60dB below max signal level
B(-3dB) = BW 3dB below max signal level
Eq (2.25)

15. Sensitivity
The sensitivity of the receiver is a measure of its ability to receive and amplify weak signals that is the minimum RF level that can be detected to produce a useable demodulated information.
The amount of gain a receiver has determines its sensitivity.
Gain is often defined as in terms of the signal voltage amplitude that must be applied to the receiver’s input to provide a standard output power, measured at the receiver’s output terminals.

16. Cntd…
Generally the SNR and the output power of the audio stage determine the quality of received signal and whether it is usable.
For commercial AM broadcast-band receiver SNR ≥ 10dB with (1/2 W) 27dBm output power of audio section is usable.
For broadband microwave receivers: SNR ≥ 40dB with (5mW) 7dBm is minimum acceptable value.

17. Cntd…
The sensitivity or threshold of a receiver is usually stated in Volts. An AM broadcast-band receiver is 50 V, two-way mobile radio receiver is btw 0.1 V to 10 V.
The sensitivity also depends on input noise power, noise figure (NF) and the BW improvement factor of the receiver.
The best way to improve the sensitivity of a receiver is to reduce the noise level by reducing the temperature or the BW of the receiver or by improving the NF.

18. Bandwidth Improvement (BI)
Thermal noise is the most prevalent form of noise and directly proportional to BW.
Reduce BW ~ reduce noise, improving system performance but receiver BW must exceed the BW of information.
When signal propagates from antenna thru the RF section and IF section, the BW is reduced, thus reducing the noise.

19. Cntd…
The SNR is calculated at a receiver input using the RF BW for noise power measurement.
The noise reduction ratio is achieved by reducing the BW is called bandwidth improvement (BI) and is expressed mathematically as
The corresponding reduction in the noise figure due to the reduction in BW is called noise figure improvement and is expressed mathematically in dB as
Eq (2.26)
Eq (2.27)

20. Example 1
Determine the improvement in the NF for a receiver with an RF bandwidth equal to 200 kHz and an IF bandwidth equal to 10 kHz.

21. Dynamic Range
The difference (in dB) between the minimum input level necessary to discern a signal and the input level that will overdrive the Rx and produce distortion.
Input power range over which the Rx is useful.
A dynamic range of 100dB is considered about the highest possible.
A low dynamic range can cause a desensitizing of the RF amplifiers and result in severe intermodulation distortion of the weaker input signal.

22. Fidelity
A measure of the ability of a communication system to produce (at the output of the Rx) an exact replica of the original source information.
Forms of distortion that can deteriorate the fidelity of a communication system:-
Amplitude
Frequency
Phase

23. Linear gain, 1-dB compression point, and third-order intercept distortion for a typical amplifier.
Figure 37

24. Insertion Loss (IL)
IL is a parameter associated with the frequencies that fall within the passband of a filter.
The ratio of the power transferred to a load with a filter in the circuit to the power transferred to a load without the filter.
IL (dB) = 10 log (Pout /Pin)
Eq (2.28)

25. Noise Temperature & Equivalent noise Temperature
Thermal noise directly proportional to temperature ~ can be expressed in degrees, watts or volts.
Environmental temperature, T (kelvin)
T = N/KB
Where N = noise power (watts)
K = Boltzman’s Constant
(1.38 X J/K)
B = Bandwidth (Hz)
Eq (2.29)

26. Cntd… Equivalent noise temperature, (Te) Te = T(F-1)
Where T = environmental temperature
(kelvin)
F = Noise factor
Te often used in low noise, sophisticated radio receivers rather than noise figure.
Eq (2.30)

27. Several values of NF, NR and Te for an environment temperature of 17oC (290oK)
Table 2

28. Types of Radio Receivers
Two basic types of radio receivers.
Coherent
Synchronous receivers
The frequencies generated in the Rx & used for demodulation are synchronized to oscillator frequencies generated in Tx.
Non-coherent
Asynchronous receivers
Either no frequencies are generated in the Rx or the frequencies used for demodulation completely independent from the Tx’s carrier frequency.
Non-coherent detection = envelope detection.

29. Cntd…
Various types of radio receivers have been proposed but only two types remain survived over the rest.
Tuned Radio Receiver (TRF)
Superheterodyne Receiver (SHR)
Both are non-coherent receivers
SHR is in general use and TRF still found in fixed-frequency applications.

30. The TRF Receiver
Used primarily today as a fixed-frequency receiver in special applications, where it offers simplicity and high sensitivity.
If a single RF amplifier is used, the BW is too wide to reject all frequencies except the desired one.
More typically, more RF amplifiers, all tuned together, are used. This configuration decrease the BW to a point where only the one desired frequency will be passed to the detector.

31. Cntd…
The selectivity is determined by the BW of RF amplifiers and RF amplifiers provide amplification for the desired signal.
Sensitivity and selectivity (two important characteristics in all receivers) are increased by additional RF amplifiers.
TRF receivers have limitations in their usefulness to single-channel, low-frequency applications.

32. Block Diagram of a TRF Receiver
Figure 38

33. Disadvantages of TRF receivers
Bandwidth inconsistency and varying center frequency when tuned over a wide range of input frequencies – the BW of the RF amplifiers increases as the operating frequency increases (with Q remains relatively constant) i.e BW = fc/Q.
Instability – It is extremely difficult to get all the RF amplifiers tuned to exactly the same frequency across the entire AM broadcast bands (535 kHz to 1605 kHz).
Their gains are not uniform over a very wide frequency range because of non-uniform L/C ratios of the transformer-coupled tank circuits in the RF amplifiers.

34. Example 2
For an AM commercial broadcast-band receiver (535 kHz to 1605 kHz) with an input filter Q-factor of 54, determine the BW at the low and high ends of the RF spectrum.

35. The Superheterodyne Receiver
The non-uniform selectivity of TRF led to the development of superheterodyne receiver near the end of World War 1.
Heterodyne means to mix two frequencies together in a nonlinear device or translate one frequency to another using nonlinear mixing.
The principle of fixed tuning is used in SHR, which mixes the incoming RF signal with a signal generated within the receiver.

36. Non-coherent AM Superheterodyne Receiver Block Diagram
Figure 39

37. Cntd…
The mixing produces a difference frequency, usually a lower frequency than received RF signal called intermediate frequency, fIF.
IF signals for commercial AM broadcast are frequencies between 450 kHz to 460 kHz.
IF signals fall between the RF and original source information frequencies.
The local oscillator (LO) is designed such a way that its frequency, fLO is always above or below the desired RF carrier by an amount equal to the IF center frequency.

38. Cntd…
The adjustment for the center frequency of the preselector and fLO are gang-tuned.
Gang tuning means that the two adjustments are mechanically tied together so that a single adjustment will change the center frequency of the preselector and fLO.
If the fLO is tuned above the RF frequency it is called high-side injection.
If the fLO is tuned below the RF frequency it is called low-side injection.

39. Cntd…
In AM broadcasting receivers, high-side injection is always used.
Mathematically the LO frequency is
For low-side injection: fLO = fRF + fIF
For high-side injection: fLO = fRF – fIF
fLO = local oscillator frequency (Hz)
fRF = radio frequency (Hz)
fIF = intermediate frequency (Hz)
Eq (2.31)

40. Superheterodyne receiver RF-to-IF Conversion
Figure 40

41. Example 3
For an AM superheterodyne receiver that uses high-side injection and has a local oscillator frequency of 1355 kHz, determine the IF carrier, upper side frequency and lower side frequency for an RF wave that is made up of a carrier and upper and lower side frequencies of 900 kHz, 905 kHz and 895 kHz respectively.

42. Figure for Example 3
Figure 41

43. Image frequency
An image frequency (IMF) is any frequency other than the selected RF carrier that, if allowed to enter a receiver and mix with the LO, will produce a cross-product frequency that is equal to the IF.
It is equivalent to a 2nd RF that will produce an IF that will interfere with the IF from the desired RF.
Once an IMF has been mixed down to IF, it cannot be filtered out or suppressed.

44. Cntd…
If the selected RF carrier and its IMF enter a receiver at the same time, they both mix with the LO and produce difference frequencies that are equal to the IF.
Hence two difference stations are received and demodulated simultaneously, producing two sets of information frequencies.
For high-side injection (HSI): fIF = fLO – fRF
Hence the IMF (fIM) is the RF located in the IF frequency above the LO.
Mathematically with HSI: fIM = fLO + fIF
Since the desired RF equals the LO minus the IF,
fIM = fRF + 2fIF
Eq (2.32)
Eq (2.33)

45. Spectrum of Image frequency using HSI
Figure 42

46. Image Frequency Rejection Ratio (IMFRR)
From Figure the higher the IF, the farther away in the spectrum the IMF from the disired RF.
Hence for better image-frequency rejection (IMFRR), a high IF is preferred.
However the higher the IF the more difficult it is to build stable amplifiers with high gain.
Therefore there is a trade-off when selecting the IF for a radio receiver between IMFRR and IF gain and stability.

47. Cntd…
The IMFRR is a numerical measure of the ability of a preselector to reject the image frequency.
For a single-tuned preselector, the ratio of its gain at the desired RF to the gain at the image frequency is the IMFRR.
If there is more than one tuned circuit in the front end of the receiver, the total IMFRR is simply the product of the two ratios
Eq (2.34)

48. Example 4
For an AM broadcast band superheterodyne receiver with IF, RF and local oscillator frequencies of 455 kHz, 600 kHz and 1055 kHz respectively, determine
(a) Image frequency.
IMFRR for a preselector Q of 100.

49. Frequency conversion for Example 4
Figure 43

50. Example 5
For a citizens band receiver using high-side injection with an RF carrier of 27 MHz and an IF center frequency of 455 kHz, determine
(a) Local oscillator frequency.
(b) Image frequency.
(c) IMFRR for a preselector Q of 100.
(d) Preselector Q required to achieve the same IMFRR as that achieved for an RF carrier of 600 kHz in Example 3.

51. Frequency spectrum for Example 5
Figure 44

52. Image frequency rejection
IMF must be rejected prior to the mixer/converter stage.
Image frequency rejection is the primary purpose of RF preselector.
A proper RF and IF filtering can prevent an image frequency from interfering with the desired RF.
The ratio of RF to IF is an also important consideration for IMF rejection.
The closer the RF to IF, the closer the RF to IMF.
Figure 45

53. Signal to noise power ratio:
SNR

54. Noise
Probability of distribution of Noise is considered uniform over the frequency band –B to +B = 2B.
It is assumed to be distributed for negative frequencies also.
Noise power per hertz: is No/2 watt/Hz.
Noise over the frequency band B is
No/2 watt/Hz x 2B Hz = NoB watt

55. Baseband noise
A signal of power PT watts is present in the band –W to +W (Hz).
The channel bandwidth is –B to +B Hz in which the noise is uniformly No/2 watts/Hz making total noise power NoB watts.
SNR is PT/ NoB.
Figure 46

56. Cntd…
Passing the spectra through a LPF of BW 2W Hz , the modified noise level is NoW watt.
Thus the noise level is reduced by a factor B/W.
Deduction: a suitable filter improves on noise level.
Figure 47

57. Effect of noise on AM carrier
Characteristics of vector of modulated signal vmod are well defined.
The noise vector n(t) is uncorrelated to vmod. It can take any angle  depends on n.
In case noise level is assumed constant, path of n(t); so also the path of composite vector r(t) will be on the circle.
Figure 48

58. Narrow band noise: Band limited by LPF/ BPF.
Noise is assumed to have uniform distribution.
A narrow band noise is the result of noise at the output of LPF or BPF provided that the critical frequency o lies any where on the “channel’s band”.
In narrow band, where the signal bandwidth to carrier ratio is very small, the noise can be conveniently represented as:
Where (t) is the phase of the noise wrt , is a random function of time.
n(t) can be expanded as
n(t)=s(t)cos((t))cos(ot+) - s(t)sin((t)) sin(ot+)
Taking nc= s(t)cos((t)),
ns= s(t)cos((t)) and
o= c

59. Noise added to signal n(t)=s(t) cos(ot++ (t) ) can be expressed as
n(t) = nc(t) cos(ct+) - ns(t) sin(ct+)
And vmod(t) = AcVm(t) cos (ct+)
Signal at the noise limiting filter of the receiver output is
r(t)= vmod(t) + n(t)
= AcVm(t) cos (ct+) +nc (ct+) -nssin (ct+)
= { AcVm(t)+nc}cos(ct+) - nssin (ct+)

60. Noise at the o/p of DSB-SC input filter
The modulated signal is
Vdsb(t) = Acm(t) cos (ct+)
The signal with transmission noise is fed at the input of the BPF. At its output, the signal is:
vdsbfil(t) ={ Acm(t)+nc}cos(ct+) - nssin (ct+)
Here:
the signal power is = Ac2m2/2
the noise power is = nc2/2 + ns2/2 = 2N0W
SNRBPF at the output of BPF = Ac2 m2/4NoW

61. SNR of DSB-SC at the output of coherent detector
This vdsbfil(t) is passed through a coherent demodulator followed by a LPF. The output is:
Vdsb_dem(t) = vdsbfil(t).cos(ct+)
The output vd(t) is the result of filtering the higher frequencies components from vdsb_den(t).
Vd(t) = Acm(t)+nc
SNRD= Ac2 m2/2NoW
Overall SNR improvement = SNRD/SNRBPF = 2.

62. SSB demodulator
The calculations uses Hilbert transformation, not discussed.
It is stated that the SNR in SSB is same as DSB.
The effect of loss of coherency/phase error is much more in case of SSB.

63. Noise at the o/p of AM input filter
The modulated signal is
Vam(t) = Ac(1+m(t)) cos (ct+)
The signal with transmission noise is fed at the input of the BPF. At its output, the signal is:
vdsbfil(t) ={ Ac(1+ m(t))+nc}cos(ct+)- nssin (ct+)
Here:
the signal power is = Ac2(1+m2)/2
the noise power is = nc2/2 + ns2/2 = 2N0W
SNRBPF at the output of BPF=Ac2(1+ m2)/4NoW

64. SNR of AM at the output of coherent detector
This vamfil(t) is passed through a coherent demodulator followed by a LPF. The output is:
Vdsb_dem(t) = vamfil(t).cos(ct+)
The output vd(t) is the result of filtering the higher frequencies components from vdsb_den(t).
Vd(t) = Acm(t)+nc
SNRD= 2Ac2 m2/4NoW
Overall SNR improvement = SNRD/SNRBPF = 2.

65. Noise performance of AM envelop detector
r(t)=Ac[1+m(t)]cos (ct+) +nccos(ct+) - nssin (ct+)
= {Ac[1+m(t)]+nc} cos(ct+) - nssin(ct+)
Rendering r(t) = {Ac[1+m(t)] +nc(t)} cos (ct)
This yields output y(t) = Acm(t) +nc(t)
According to above equation, the SNR of envelop detector and coherent detector seems same.
It depends on one more factor, modulating index. For low modulating index, noise power dominates at the output of the input BPF resulting in poor SNRfil..

66. Cntd…
After a particular level, threshold level, the output of the detector looses the relationship with input.
The overall performance is then much degraded and is difficult to be calculated.