# Part 2: Receiver and Demodulator

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1 University of Pennsylvania Department of Electrical and Systems Engineering ESE06: Electrical Circuits and Systems II Lab Amplitude Modulated Radio Frequency Transmission System Mini-Project Part : Receiver and Demodulator Introduction This mini-project is the continuation of the AM Radio Transmission System lab you did earlier. In this lab you will build the receiver section (part ), shown in Fig. 1 below. The goal of the circuit of part is to recover the modulation signal vm(t) that contains the information of interest (e.g. the voice or music transmitted over the radio waves). Figure 1: Elements of a basic AM Radio Transmission System You will learn how to demodulate an AM signal, using a peak detector (or envelope detector), and how to amplify this signal using an audio amplifier. Once you have built these elements you will put the modulator (built during part 1) and the demodulator together and test out the overall system of Fig March 8, 005

2 This lab is more ambitious than any of the previous labs. It makes use of your knowledge gained during the previous labs. In order the finish on time, you will need to prepare the pre-lab carefully and review part 1 ( AM Transmitter/Receiver of this mini-project). Distortion Signals undergo distortion as a result of non-linearity in the circuits. A good system should introduce as little distortion as possible. When you did part 1 of this lab, you noticed that the modulated signal could get distorted when the modulator is not adjusted properly. Further distortions will be introduced during the demodulation process. In this lab you will learn how to specify the amount of distortion of a signal. However, first lets introduce some basic concepts about distortion. We will consider a pure sinusoidal signal. When no distortion occurs the spectrum of this signal should be a component at the frequency of the sinusoid (called the fundamental frequency f 0 ), shown in Fig. a. As a result of non-linearities that are introduced at several stages of the processing chain, the signal won t be a pure sinusoid anymore. This results in a spectrum that has components besides the fundamental frequency f0. These frequency components are usually at multiples of the fundamental frequency and are called harmonics. For instance the components at f 0, 4f 0, etc. are called the even harmonics while the ones at 3f 0, 5f 0, etc. are called odd harmonics. Fig. b shows the spectrum of a distorted sinusoid. The larger harmonics the spectrum has the larger the distortion of the pure sinusoid will be. Figure : Spectrum of (a) a pure sinusoid and (b) a distorted sinusoid. Total Harmonic Distortion (THD) The distortion is usually expressed by the quantity, called total harmonic distortion or THD. This is defined as the ratio of the power in the harmonics over the power of the signal. The power is related to the square of the amplitude of the frequency components. This allows us to write the THD (%) as, March 8, 005

3 THD V ( f 0 ) V (3 f0 ) V (4 f0 ) V ( f ) 0 V (5 f 0 )... (1) Since the THD is obtained by taking a ratio, it does not matter whether the amplitude is expressed in RMS or as a peak amplitude. As can be seen in Fig., the magnitude of the frequency components in the spectrum is usually given in db. In order to find the magnitude (in V) of each component one has to convert from db into voltage. This can be easily done through the definition of db: A = 0.log10(V) (in db) () or V = 10 A/0 (in Volt) (3) As can be seen from Eq. (1) the THD is given by the ratio of the harmonics over the fundamental component. This implies that the difference in db between the fundamental and the harmonics determines the amount of distortion. One can give the fundamental component a reference level of e.g. 0 db. An example is shown in the figure below. Figure 3: Spectrum of a distorted sinusoid with fundamental frequency f0=1.68khz. The fundamental frequency is f 0 =1.68kHz. The two most pronounced harmonics are the nd and the 3 rd ones which are each about 6.5dB below that of the fundamental component. Using the expressions (1) and (3) one finds that the THD of 6.7%. This is a pretty bad THD. For high quality audio systems the THD is typically 0.01% and for digital audio systems is may be as low as 0.00% over the audio frequency range from 0 to 0 khz. 3 March 8, 005

4 Receiver with peak detector and audio amplifier The details of the receiver circuits are shown in Fig. 4. The first section consists of an antenna and a LC tuned filter followed by a wide-bandwidth amplifier (LF 356 with a gain-bandwidth product of 5 MHz). The tuned circuit selects the carrier frequency. The next section is a simple peak detector that is used to demodulate the AM signal. It consists of a diode followed by a capacitor in parallel with a resistor (see section3.5.4 Rectifier with a Filter Capacitor or Peak Detector in the textbook by Sedra-Smith, 5 th ed.). This circuit, also called an envelope detector, extracts the modulating signal. The final stage is an audio amplifier. We have implemented this with an operational amplifier that has a gain of 10. Notice that a coupling capacitor C c (also called a DC blocking capacitor) has been added after the peak detector. This is done to block the DC component in the rectified signal. This DC component does not carry information and can saturate the audio amplifier. Also, the speaker is connected through a coupling capacitor C 3 to the output of the amplifier. The audio amplifier is usually a power amplifier that is capable to deliver sufficient power to the speakers. For the purpose of this lab, we are using the 741 as an audio amplifier. This is done since we are not interested in providing a lot of power to the speaker in contrast to a conventional audio amplifier that is designed for large power delivery. When you measure your circuit you will notice that you won t be able to deliver a large signal to the speaker since the op-amp won t be able to deliver the necessary current (but for our purpose that is ok). Figure 4: Receiver circuit consisting of an amplifier stage, a peak-detector and an audio amplifier. The peak detector, shown in Fig. 5 can be considered as a half-wave rectifier with a lowpass filter (RC circuit). The value of the RC circuit determines the peak-to-peak value of ripple V r of the rectified signal, according to the following expression, V r 1 / f R C c 3 V ( 1 e ) (4) p 4 March 8, 005

5 in which V p is the peak value of the incoming, signal and f c the frequency of the signal. When using the circuit to demodulate an AM signal, the RC time constant is chosen such that, f C > 1/ R 3 C > f m (5) in which fc and fm is the carrier and modulating frequency, respectively. The first condition determines the ripple of the signal while the second inequality assures that the modulating signal with frequency fm passes through the peak detector (notice that the R3- C circuit forms a low pass filter. To keep the ripple small, you want to make sure that the you select the R 3 C such that f C >> 1/ R 3 C without violating the second condition (1/ R3C > fm). This condition assures that the modulating signal will pass without being attenuated by the parallel R3C circuit. Figure 5: Envelope or peak detector We will use as the carrier signal a sinusoid with a frequency f c of about 100 khz and as the modulation signal a sinusoid with frequency f m of about 5000 Hz. Pre-lab assignment 1. Read the introduction of part 1 on AM Radio Frequency Transmission System. Consider the following spectrum of a distorted sinusoid. Calculate the THD (in %) of this signal. Show how you got your result. Figure 6: Spectrum of a distorted sinusoidal signal of 5 khz. 5 March 8, 005

6 3. Read the section on peak detectors in your textbook section (Microelectronics by Sedra and Smith). 4. The LF356 amplifier has a gain bandwidth product of 5 MHz. What is the bandwidth of the inverting RF amplifier configuration shown in Fig. 4? 5. Design of a peak detector: a. Find the value of C and R 3 of the peak detector (Fig. 5), using expression (5). Use a value of R 3 in the range of -10 kohm and select a capacitor according to expression (5). b. For the selected values of R3 and C calculate the corresponding ripple V r /V p (see expression (4). Assume a frequency f c of 100 khz. 6. Design the audio amplifier, shown in Fig. 4 such that it has a gain of 11. Use resistor values in the range of 1 to10 kohm. 7. Coupling capacitor C3: a. What is the role of the coupling capacitor? b. This capacitor forms a high pass filter. What is the lowest frequency that can be passed un-attenuated, assuming that the speaker has a resistance of 8 Ohm? In-lab assignment 1 OpAmp LF356 Op-Amp 1 Diode Inductor 1 Capacitors: 47 uf and others (TBD) Capacitors: 0.1 uf as decoupling caps 1 Resistors: 5.1k, 40 kohm and others (TBD) 1 Potentiometer of 50 kohm Note: You will be using the modulator circuit that you constructed during the first part of this mini-project (Fig. 7 part 1). Procedure: 1. Check that you still have the modulator circuit of the first part of this mini-project, shown below. You should add a decoupling capacitor between the two power supply pins (7 and 4) of the op-amp and the ground. Connect all ground wires to a single point on your protoboard to reduce the noise. 6 March 8, 005

7 Figure 7: AM Modulator/transmitter circuit (built during part 1 of the project).. Next you will construct the receiver and demodulator circuit of Fig. 4. Construct this circuit in a corner of the protoboard as far from the modulator circuit as possible to reduce interference. Start with the tuned LC circuit that you designed earlier in part 1 of the project. 3. Construct the amplifier using the LF356 as shown in Fig. 4. The pins of the amplifier are given in the parts list (Fig. 7). Use a voltage of +1V, and 1V for the power supply. Place 0.1 uf decoupling caps between the power supply pins ( 4 and 7) and ground. Check that the amplifier functions properly. You can apply a small input voltage and measure the output voltage. Notice that the amplification is about 50. Do not saturate the amplifier. 4. Construct the peak detector. Use for the resistor R3 a 50 kohm potentiometer, so that you can adjust the resistor value to optimize the rectified and filtered signal. Be careful to use short connections and use a single point to which you connect all the grounds of your instruments and circuit. When finished, you should ensure that the receiver works properly. You can apply a small AM modulated sinusoidal signal at the input of the operational amplifier and verify the operation. To generate the AM signal, use the HP Function generator and select an AM signal (carrier frequency of 100 khz, modulation frequency of 5000 Hz and modulation depth of 50%). Display the AM signal and the output of the peak detector on the oscilloscope. Take a snapshot of the waveforms. [For use of the function generator see: 7 March 8, 005

9 Report: Under the experimental results include: a. RF amplifier and peak detector. i. Circuit with component values. ii. Measured output characteristic for an AM input signal. b. Audio amplifier: i. The circuit ii. Output signal for an AM input signal iii. Spectrum of the output signal, corresponding to the time domain signal shown in ii. above. c. Calculation of the power delivered by the audio amplifier to the 8 Ohm resistor (speaker) for the signal shown in ii above. d. Calculation and value of the THD of the output signal. Modified and Updated by Jan Van der Spiegel March 1, March 8, 005

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