Square Law Demodulator Advantages and Disadvantages

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 block diagram of the quadratic distribution demodulator is shown in Fig. 2. Let`s start with the meaning of “square distribution” in the square distribution modulator: “square distribution” refers to the input-output ratio of the device used for modulation. Let`s say we want a product modulator. Let c(t) and m(t) respectively carriers and message signals (modulating). Carrier is a pure sinusoid of frequency fc. The expected performance of a product modulator is c(t).m(t), the product.

It uses nonlinear devices like transistors or diodes where the input and output characteristics maintain a nonlinear relationship like: v2(t) = a1v1(t) + a2v12(t), where a1 and a2 are constants. v2(t) is the output of a nonlinear device. v1(t) is the input to the nonlinear device. The block diagram looks like this:The circuit that generates the AM waves is called the amplitude modulator. The generation of AM waves using the quadratic distribution modulator could be better understood by observing the quadratic distribution modulator circuit shown in the figure above. It consists of the following elements: By comparing the output of the quadratic distribution modulator with the standard equation of the AM wave, we obtain the scale factor $k_1$ and the amplitude sensitivity $k_a$ as $frac{2k_2}{k1}$. 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. The input-output characteristics, i.e.

the transfer properties of a quadratic distribution demodulator are nonlinear and are expressed mathematically as: There are two types of AM detectors or demodulators such as: The AM diode detector is an envelope detector – it provides an output of the signal envelope. As such, the diode detector or demodulator is capable of providing an output proportional to the amplitude of the amplitude of the amplitude modulated signal envelope. The AM diode envelope detector has been available for many years. It is widely used. Although amplitude modulation is less used nowadays and other forms of AM detector can be easily integrated into integrated circuits, the simple diode detector still has some advantages. The envelope demodulator consists of a diode and an RC filter. Although its simplicity has been the main reason for its widespread use, its performance is not as good as that of other types of AM detectors/demodulators, especially in terms of distortion levels. The switching modulator is similar to the quadratic distribution modulator. The only difference is that with the rectangular modulator, the diode works in non-linear mode, while with the switching modulator, the diode must function as an ideal switch. 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.

The input-output waveforms of the envelope demodulator are shown in Fig. 4. In each positive half-cycle of the input, the demodulating diode is polarized forward and charges the connected filter capacitor C via the load resistor R to almost the maximum value of the input voltage. The modulating signal and carrier are connected in series and their sum V1(t) is applied to the input of the nonlinear device, such as diode, transistor, etc. Thus………………………. (1) The input-output relationship for nonlinear devices is as described in:…………………. (2)where a and b are constants. Now, if we replace the expression (1) in (2), we get Now, by replacing the expression (1) in (2), we get Or,Or,The five terms of the expression for V2(t) are as follows: Term 1: ax(t) : Modulating signalTerm 2 : a Ec cos (2π fct) : Signal porteTerm 3 : b x2 (t) : Modulating signal squareTerm 4 : 2 b x(t) cos ( 2π fct ) : AM wave only with sidebandsTerm 5: b Ec2 cos2 (2π fct): Squared transporterOf these five terms, terms 2 and 4 are useful, while the other terms are not useful.

If we replace the expression (1) by (2), we get Or,Or,Therefore, the output voltage vo(t) contains only the useful terms. or, therefore, ,………………………… (3) If we compare this to the expression for the standard AM wave, i.e. we find that the expression for Vo(t) of equation (3) represents an AM wave with m = (2b/a). Therefore, the quadratic distribution modulator generates an AM wave. Disadvantages of the square law modulator: 1) Since nonlinear devices are used, it only works in the nonlinear region of the characteristic curve. 2) The bandpass filter has to set fc, which is ideally difficult. The standard AM wave is applied to the input of the demodulator. The envelope demodulator is a simple and highly efficient device suitable for detecting a narrowband AM signal.

This signal $V_1t$ is applied as input to a nonlinear device such as a diode. The properties of the diode are closely related to the law of squares. The AM diode detector can be built from a single diode and a few other components and is therefore a very cost-effective circuit block in an overall receiver. In the early days of radio, these signal detectors were made with discrete components, but modern radios use integrated circuits with built-in detectors. A narrowband AM wave is one where the carrier frequency fc is much higher relative to the bandwidth of the modulating signal. The ratio between the desired signal and the unwanted signal is given by: This signal $V_1left ( t right )$ is created as the input of the diode. For example, suppose the size of the modulating signal is very small compared to the amplitude of the carrier signal $A_c$. The ON and OFF action of the diode is therefore controlled by the carrier signal $cleft( t right )$. This means that the diode is polarized forward when $cleft (tright)>$0 and it is polarized inversely when $cleft (tright) usually a resistor is placed above the capacitor – this can be either the charge of the next stage, a volume control or a resistor in the circuit. This level must be determined by calculating the time constant of the capacitor and the load.

This should be done between the RF signal and the audio modulation so that the RF is satisfactorily removed, but the audio modulation remains intact. When the input signal becomes larger than the capacitor voltage, the diode redirects and the process repeats. The representation of this periodic pulse train in the Fourier series is Note that in this circuit, the secondary side of the transformer provides a continuous return to earth. Sometimes when the AM signal detector is used with a capacitor connection in the previous step, a ground resistor or choke (inductor) must be used at the input to provide a DC return path.

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