Square Law Demodulator Circuit
The block diagram of the quadratic distribution demodulator is shown in Fig. 2. The envelope demodulator is a simple and highly efficient device suitable for detecting a narrowband AM signal. Here we assumed that the diode is ideal and that the AM wave applied to the input of the demodulator is provided by an internal resistance source Rs. An envelope demodulator produces an output signal that closely follows the envelope of the input AM signal. It is used in all commercial AM radio receivers. The input-output waveforms of the envelope demodulator are shown in Fig. 4. Of these terms, the only desired term bEc2 is mx(t), which is due to the term b v12. Therefore, the name of this demodulator is quadratic demodulator. There are two types of AM detectors or demodulators such as: Input-output characteristics, i.e.
The transfer properties of a quadratic distribution demodulator are nonlinear and are expressed mathematically as: The standard AM wave is applied to the input of the demodulator. The envelope demodulator consists of a diode and an RC filter. This type of distortion occurs when the RC time constant of the charging circuit is too long. For this reason, the RC circuit cannot keep up with the rapid changes in the modulating envelope. The diagonal section is shown in Fig. 5. We know that the mathematical relationship between the input and output of the quadratic legislator $V_1left( t right )$ is the input of the square law device, which is none other than the AM wave. In each positive half-cycle of the input, the demodulating diode is polarized forward and charges the filter capacitor C connected via the charging resistance R almost to the peak value of the input voltage. This demodulator contains a quadratic distribution and a low-pass filter. The AM wave $V_1left ( t right )$ is applied as input to this demodulator. There are two types of distortions that can occur in the output of the detector, such as: the capacitor is charged by D and Rs when the diode i is turned on and discharges by R when the diode is off. The capacitor is now discharged by R between the positive peaks, as shown in Fig.
4. The unloading process continues until the next positive half-cycle. Hello! My name is Sasmita. In ElectronicsPost.com, I pursue my love of teaching. I am M.Tech in electronic engineering and telecommunications. And if you really want to know more about me, please visit my “About” page. Read More On the other hand, the RC discharge time constant must be long enough for the capacitor to discharge slowly through the charging resistor R. However, this time constant must not be too long so that the voltage of the capacitor cannot discharge with the maximum rate of change of the envelope. This means that the distortion in the detector output is only low if the AM applied is low and the modulation percentage is very low. vo (t) = ( bEc2m ) x(t) ………………. (3) Therefore, at a higher modulation depth of the transmitted signal, overmodulation can take place at the detector output.
Another term that goes through LPF to RL load resistance is 1/2[bEc2m2 x2 (t)]. A narrowband AM wave is one where the carrier frequency fc is much higher relative to the bandwidth of the modulating signal. where v1(t) = detector input voltage = AM wave Negative peak clipping occurs as a result of this overmodulation, as shown in Fig. 6. It shows the charge discharge of the filter capacitor and the approximate output voltage. In the positive half-cycle of the AM wave, the diode conducts and the capacitor charges to the maximum value of the AM wave. If the AM wave value is less than this value, the diode is polarized in the opposite direction. Thus, the capacitor discharges through the resistance R until the next positive half-cycle of the AM wave. If the value of the AM wave is greater than the voltage of the capacitor, the diode conducts and the process is repeated. If we now replace v1(t) in equation (1), we get The ratio between the desired signal and the unwanted signal is given by: This distortion occurs because the modulation index on the detector output side is higher than on the input side.
The charging time constant RsC must be short compared to the carrier period 1/fc. When the input signal becomes larger than the capacitor voltage, the diode redirects and the process repeats. This is an unwanted signal that results in signal distortion. As soon as the capacitor is charged to the peak value, the diode stops conducting. We need to select the values of the components so that the capacitor charges very quickly and discharges very slowly. As a result, we get the voltage waveform of the capacitor, which corresponds to the envelope of the AM wave, which is almost similar to the modulating signal. This means that we have restored the x(t) message signal to the detector output. This envelope detector consists of a diode and a low-pass filter. Here, the diode is the main sensing element. Therefore, the envelope detector is also called a diode detector. The low-pass filter contains a parallel combination of resistor and capacitor. From these waveforms, it can be observed that the envelope of the AM wave is successfully restored.
This ratio should be maximized to minimize distortion. To achieve this, we must choose |mx(t)| low from unit (1) for all values of t. If m is small, then the AM wave is weak. The process of restoring the message signal from the received modulated signal is called demodulation. This detection process is exactly opposite to that of modulation. This desired term is extracted after the diode using a low-pass filter (LPF), as shown in Fig. 2.