The circuit that produces the AM waves is called the amplitude modulator and in this post we will discuss two of these modulator circuits, namely: the modulating signal and the 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. 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: Both circuits use a nonlinear element such as a diode for their implementation. Both modulators are low-power modulator circuits. AM wave generation with the rectangular law modulator could be better understood by observing the quadratic law modulator circuit shown in Fig.1. Therefore, the quadratic distribution modulator generates an AM wave. Of these five terms, terms 2 and 4 are useful, while the other terms are not useful.
In other words, the charging voltage v2(t) varies periodically between the values v1(t) and zero with the rate corresponding to the carrier frequency fc. How to Build Your Own AlphaZero AI with Python and Keras Please subscribe to Electronics Post Channel if you like my tutorials. The modulating signal x(t) and the sinusoidal carrier signal c(t) are connected in series. Therefore, the input voltage to the diode is given by: Therefore, the output voltage vo(t) contains only the useful terms. 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 The LC tuned circuit acts as a bandpass filter. Its frequency response is shown in Figure 2, which shows that the circuit is tuned to the frequency fc and its bandwidth is equal to 2fm. This bandpass filter eliminates unnecessary terms from the equation v2(t). We find that the expression for Vo(t) of equation (3) represents an AM wave with m = (2b/a). Motivated researchers who make AI the most efficient and provide better equipment for India. If we now replace the expression (1) in (2), we get the club terms 2, 4 and 1, 3, 5 as follows to obtain, Therefore, the output voltage is v2(t) = v1(t) in the positive half-cycle of c(t) and v2(t) = 0 in the negative half-cycle of c(t). This is the required expression for the AM wave with m=[4/πEc]. Undesirable terms can be eliminated with a bandpass filter (BPF). If you compare this with the expression for the standard AM wave, that is, if you put the second and third terms together, you get The five terms of the expression for V2(t) are as follows: It is assumed that this diode functions as a switch. The input-output relationship for nonlinear devices is as follows: The amplitude of the carrier is much greater than that of x(t) and c(t) determines the state of the diode (ON or OFF).
A comprehensive practical guide to transferring learning with real-world applications in deep learning 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. Let us express gp(t) using the Fourier series as follows: The odd harmonics of this expression are undesirable and are therefore considered eliminated. Term 4: 2 b x(t) cos ( 2π fct ): AM wave with only side bands Suppose the diode acts as an ideal switch. Therefore, it acts as a closed switch when it is polarized forward in the positive half cycle of the carrier and does not provide impedance. While acting as an open switch when biased backwards in the negative half cycle of the wearer, providing infinite impedance. In this expression, the first and fourth terms are undesirable terms, while the second and third terms together represent the AM wave. where gp(t) is a sequence of periodic pulses of the duty cycle corresponding to half a cycle period, i.e. T0 /2 (where T0 = 1/fc).