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N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II Detection or Demodulation of FM Signals: FM detector or demodulator is a device which produces an output voltage that varies linearly with the instantaneous frequency of input signal. A frequency detector is also known as Discriminator. Based on the principle of operation, FM demodulators are categorized as follows: 1. FM to AM converters 2. Phase Shift Discriminators 3. Zero Crossing Detectors FM to AM Converters: Consider the equation of a frequency modulated carrier signal: xc (t) = Ac Cos {2πfct + 2πfΔ∫ m(t)dt} Differentiating with respect to “t” d/dt {xc (t)} = - Ac Sin {2πfct + 2πfΔ∫ m(t)dt} d/dt {2πfct + 2πfΔ∫ m(t)dt} d/dt {xc (t)} = - Ac Sin {2πfct + 2πfΔ∫ m(t)dt} x {2πfc + 2πfΔm(t)} d/dt {xc (t)} = - 2πAc {fc + fΔ m(t)} Sin {2πfct + 2πfΔ∫ m(t)dt} In the above equation the factor fc + fΔ m(t) represents the instantaneous frequency of the modulated signal i.e. f(t) = fc + fΔ m(t) So, d/dt {xc (t)} = - 2πAc f(t) Sin {2πfct + 2πfΔ∫ m(t)dt} This equation shows that the derivative of FM signal is an amplitude and frequency modulated signal. But, a most significant property of the above equation is that the amplitude of the signal is proportional to the instantaneous frequency of input signal. Hence, if the derivative of the FM signal is fed to an envelope detector then the actual signal can be extracted. Therefore a conceptual block diagram of FM to AM converter can be given as: Since FM signal has a constant amplitude, therefore it is first fed to an amplitude limiter to remove any amplitude variations due to noise. Following two blocks perform the functions described above. Finally a dc block removes any dc offset from the demodulated signal. Practical Circuits: FM to AM converters are actually implemented using tuned circuits. Consider an LC circuit tuned at frequency fo. Output voltage characteristics of this circuit versus frequency can be given as: N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II This graph shows that at frequencies below fo the slope of the curve can be approximated to a straight line. Hence, in this region output voltage Vo of the LC circuit varies linearly with the frequency. This method is also known as Slope Detection. The only problem in this circuit is that the linear region is very small. Frequency deviations beyond this region suffer considerable distortion. It is obvious from the above graph that fo must be higher than carrier frequency fc and fc should lie somewhere in the middle of the linear region. The circuit diagram of a slope detector is as follows: To expand the linear operating region and accommodate larger frequency deviations balanced configuration is used. Balanced Slope Detector: This circuit is also known as Travis Detector. This circuit consists of two slope detectors, connected back to back to the opposite ends of a centre tapped transformer. So, when modulated signal is applied to the primary side of the circuit, both circuits are fed 180o out of phase. The circuit configuration is given below. The upper circuit is tuned above fc by an amount more than fΔ. Similarly, the lower circuit is tuned below fc by an amount fΔ. The output is taken across a series combination which represents the sum of individual outputs. N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II This scheme expands the linear operating range as shown in the following graph: This circuit does not require a dc block, as dc offset is cancelled. Phase Shift Discriminator: Phase shift discriminators exploit the fact that in a frequency modulated carrier phase varies linearly with integral of the message signal. Hence, FM signal can be demodulated by observing the varying phase of the carrier signal. Consider the mathematical expression of a FM carrier signal. xc (t) = Ac Cos {2πfct + 2πfΔ∫ m(t)dt} In the above equation, the instantaneous phase is: φ(t) = 2πfΔ∫ m(t)dt …………(i) Differentiating with respect to “t” d/dt {φ(t)} = 2πfΔ m(t) We know that time derivative of any function f(t) is given by: d/dt {f(t)} = limit {f(t) – f(t – Δt)}/ Δt Δt → 0 If Δt is assumed to be a very small quantity, then: d/dt {f(t)} ≈ {f(t) – f(t – Δt)}/ Δt………(ii) Using above equation, we can rewrite equation (i). d/dt {φ(t)}= {φ(t) – φ(t – Δt)}/ Δt ≈ 2πfΔ m(t) or φ(t) – φ(t – Δt) ≈ 2πfΔ Δt m(t) ……….……(iii) This equation shows that the phase shift is proportional to the message signal. Now consider the frequency modulated signal again. xc (t) = Ac Cos {2πfct + φ(t)}……..…..(iv) This signal is passed through a circuit which produces a Carrier Delay of 90o and Group Delay of Δt. So, after passing through this circuit the signal acquires following mathematical form. x’c (t) = Ac Sin {2πfct + φ(t - Δt)}…………..(v) Now, the actual FM signal xc (t) and delayed signal x’c (t) are fed to a multiplier to produce the following output: xc (t) x’c (t) = A2c Cos {2πfct + φ(t)} Sin {2πfct + φ(t - Δt)} ’ xc (t) x c (t) = ½A2c [Sin {4πfct + φ(t) + φ(t – Δt)} + Sin {φ(t – Δt) - φ(t)}] xc (t) x’c (t) = ½A2c [Sin {4πfct + φ(t) + φ(t – Δt)} - Sin {φ(t) - φ(t – Δt)}] N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II The higher frequency sine term can be filtered out using a low pass filter. Hence the final output comes out to be: YD(t) = - ½A2c Sin {φ(t) - φ(t – Δt)} If │φ(t) - φ(t – Δt)│<< π then Sin {φ(t) - φ(t – Δt)}≈ φ(t) - φ(t – Δt) Therefore YD(t) = - ½A2c {φ(t) - φ(t – Δt)} Using equation (iii) YD(t) = - ½A2c 2πfΔ Δt m(t) YD(t) = KDfΔm(t) …………...(vi) where KD = - A2c πΔt called Detection Constant. Equation (vi) represents that YD(t) to the message signal. A conceptual block diagram of the phase shift discriminator can be given as: Practical Circuit: Phase shift discriminators are implemented using modified form of balanced slope detectors or Travis detectors. This modified form uses a single resonant circuit tuned at carrier frequency fc. This design avoids the problems of tuning two resonant circuits at different frequencies to achieve a larger linear region. This circuit is known as FosterSeeley Discriminator. In Foster-Seeley Discriminator, primary winding of the transformer is connected to the centre of secondary winding through a capacitor. An inductor is attached between centres of the secondary winding and output load. A capacitor is used across the secondary to tune it at carrier frequency. If a voltage Vp is applied at the primary side then it induces a voltage Vs in the secondary side which has two components that are 180o apart. If the applied signal has a frequency fc then the secondary circuit resonates and behaves as a pure resistive circuit because at resonant frequency, XL = Xc. Thus the secondary voltage Vs and current Is are in phase. N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II The primary voltage Vp also appears directly across the inductor through the capacitor C1. This voltage is 90o out of phase from both components of Vs. Hence a phasor diagram of the voltages in the above circuit can be drawn as follows: Now the voltages across the diodes D1 and D2, which are represented by VD1 and VD2, are the vector sums of Vp and Vs/2 as shown in the above figure. It is also obvious from the figure that these voltages are equal and thus the voltage at output terminals is zero. When frequency of the signal on primary side increases from fc, the secondary circuit becomes inductive, i.e. XL > Xc jωL > 1/(jωC) In this situation Is and Vs are no more in phase. Thus, one component of the Vs lags Vp by more than 90o and other one leads it by less than 90o, maintaining their 180o separation. Now VD1 exceeds VD2 and a positive voltage appears across the output terminals as depicted in the following figure. Similarly, when the frequency of the signal applied at the primary side decreases from fc, the secondary circuit becomes capacitive, i.e. XL < Xc jωL < 1/(jωC) The phasor diagram of the voltages is now as follows which shows that V D2 is more than VD1 and output voltage becomes negative. Hence, the output voltage is varying in accordance with the message signal. Zero Crossing Detector: It is true to say that the information is hidden in the zero crossings of a frequency modulated signal. Therefore, it is possible to demodulate FM signal by observing its zero N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II crossings. A zero crossing detector circuit is also known as Pulse Averaging Discriminator. Practical Circuit: A zero crossing detector comprises of following operational blocks whose connectivity and performance is described as follows: First of all, the frequency modulated signal is fed to a hard limiter whose output is a square wave FM signal. A hard limiter basically chops off the sinusoidal carrier at a very small amplitude and thus generates an approximated square wave preserving the zero crossings of the FM signal. Limiter output is used to trigger a mono-stable multi-vibrator, which produces a short pulse v(t) of fixed amplitude A and duration τ. This pulse is produced at every upward or downward zero crossing of the limiter output wave. It is obvious that more pulses are generated as the frequency of the FM signal increases. These pulses are further fed to an integrator which evaluates the integral or average area under these pulses over a certain period of time T. This interval T is chosen so that the pulses’ frequency f(t) remains nearly constant during this period. Thus, the total number of pulses during this interval can be given as: n = T f(t) Since, the area of a single pulse is: Area = Aτ Hence; (1/ T) ∫ v(t) dt = (1/ T) nAτ = Aτ f(t) T The above equation shows that the output of the integrator is proportional to the instantaneous frequency of the FM signal. The block diagram of a zero crossing detector can be given as: Actual FM signal, hard limiter output, MVB pulses and integrator’s output which is proportional to the message signal are as follows: N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II Interference in FM Signals: Definition: “The undesirable mixing of external signals from other sources and transmitters is defined as interference.” Common Causes: Most commonly it occurs in radio communications. A receiving antenna picks up some other information bearing signals in the same frequency range. At some other occasions, the desired signal is received after a delay due to reflections from the neighboring objects. This phenomenon is known as Multi-path Propagation. The received signal, in this situation, behaves as another information bearing signal in the same frequency range and thus causes interference. It is also possible that the transmission cable catches electromagnetic radiations from other machinery or nearly laid cables. But in any case, message signal is partly or completely destroyed. Vulnerable Frequency Ranges: Since there are no amplitude variations in FM signals, therefore they are more immune to noise as compared to AM signals. But any noise or undesirable information signal whose frequency falls within the message bandwidth can damage the actual information as stated above. Consider an interfering signal with amplitude Ai having same frequency as message signal with amplitude Ac. Here we define a parameter “ρ” as follows: ρ = Ai / Ac If ρ << 1 then the interfering signal does not cause severe damage to the message and an intelligible signal is received. But, in case ρ exceeds 0.7, the interfering signal takes over and displaces the message signal. This phenomenon is known as Capture Effect, i.e. the interfering signal captures the channel and received instead of message signal. This is the most undesirable situation. We know that the high frequency components of signal possess relatively smaller amplitudes as compared to those near the center frequency. We also know that the impulses or short bursts of noise are limited in time but occupy large frequency ranges, a phenomenon known as Reciprocal Spreading. Therefore, in noise impulses high frequency components have larger amplitudes. Thus, if signal catches impulse like noise then its high frequency components are more vulnerable due to smaller amplitudes. Remedy: To prevent high frequency components from noise, a technique known as Pre-emphasis Filtering is used at transmitter side, whereas its inverse procedure called De-emphasis Filtering is done at the receiver. Pre-emphasis Filtering: A pre-emphasis filter is used prior to modulation where noise is theoretically absent. It amplifies the high frequency components of the message signal above noise level. On the N.E.D. University of Engineering and Technology Department of Electronic Engineering Lecture Notes: Communication Systems II other hand low frequency components pass through it without any amplification. Its circuit diagram is given below. The frequency f1 at which this circuits starts amplification is given by: f1 = 1 / (2R1C) For normal voice applications: R1C 75 sec Thus f1 2.1 kHz Similarly, the upper break frequency f2, to which amplification is done, can be given as: f2 = (R1 + R2) / (2R1R2C) Usually f2 comes out to be: f2 30 kHz The transfer function Hpe of the pre-emphasis filter is given below in dB scale. De-emphasis Filtering: De-emphasis filter is used after demodulator and performs the reverse function of preemphasis filtering. It attenuates the high frequency components of the message signal and produces an output proportional to the message signal. Lower frequency components pass through it without any attenuation. A typical de-emphasis filter circuit is given below: Its transfer function Hde is mathematically reciprocal of pre-emphasis filter. Hde = 1 / Hpe A Bode plot of Hde is given below.