Hi. I need to get a good grasp of the basic math of how a pure sinusoidal signal is described. At the moment I am somewhat confused, not only about the math, but the ways it can be practically applied.

Let's begin with this simple equation: ν = A sin θ. I'm not sure you could say it describes the signal. What I am sure about is that if someone sets a question and asks me to calculate ν, as long as I'm told the angle (theta) I can do it. If , in a question, A is 200V (Voltage at peak: Vp) and the sine of a given angle (22.02431 °) is 0.375: ν will be + 75V. Like I say, I'm not sure this equation has much application to circuit design. At the moment all I can say is the equation is true. Certainly there is no description of the frequency of the sinusoidal waveform.

Now, lets look at ω. This is 2πf. Well, this does describe something, the frequency of the signal. In radians per second, rather than cycles per second. But says nothing about amplitude. So, I can write f = ω or f = 2πf. so, 1 Hz = 6.28 radians per second. Time is a part of the description. I'm not sure whether this is a valid equation f (t) = 2πf (t) and if it is, what is means, or whether it has any particular application.

Here we have something else again, which looks like an attempt to describe the amplitude and the frequency: I'm looking at PLL's and I see this: A sin (2πf t + θ). It does not read ν = A sin (2πf t + θ), but I guess it could do so. Also it does not read ν (t) = A sin (2πf t + θ). So, what is going on here?

I do seem to understand when there is a situation where an exam-type of question is asked. For instance: Write the expression describing a sinusoidal signal, where the period is 20 Ms, A is 200V and ν is 75V. Okay, so the frequency is 50Hz. So, we get: +75V = 200 sin (100π + 0.375). I got the sine of theta, by dividing 75 (opposite) by 200 (hypotenuse). Of course the answer (+75V) has nothing to do with the frequency part of the equation, I mean, the 100π is ignored in the calculation of the answer. Which to me seems an odd thing. Clearly, this mathematical description is of a signal that is 22.02431 ° from the start of the cycle. That is 0.384 of a radian. So, as I have written it, the worked out equation says nothing, directly, about the phase angle. Or, the point, in terms of phase angle, at which 75V is reached. I'm assuming that + 0.375 is the correct number in the equation, and not 0.384.

I'm not at all sure why someone would devise a way of calculating ν, and half of the equation has nothing to do with the means of calculating that. Of course, A sin (2πf t + θ), which I see when looking at PLL, says nothing explicitly about calculating ν. If fact it does not look like an equation as such.

And finally, I'm not sure what is going on when I see things like: ν (t). Or f (t). Thanks if you can help. Rich

Let's begin with this simple equation: ν = A sin θ. I'm not sure you could say it describes the signal. What I am sure about is that if someone sets a question and asks me to calculate ν, as long as I'm told the angle (theta) I can do it. If , in a question, A is 200V (Voltage at peak: Vp) and the sine of a given angle (22.02431 °) is 0.375: ν will be + 75V. Like I say, I'm not sure this equation has much application to circuit design. At the moment all I can say is the equation is true. Certainly there is no description of the frequency of the sinusoidal waveform.

Now, lets look at ω. This is 2πf. Well, this does describe something, the frequency of the signal. In radians per second, rather than cycles per second. But says nothing about amplitude. So, I can write f = ω or f = 2πf. so, 1 Hz = 6.28 radians per second. Time is a part of the description. I'm not sure whether this is a valid equation f (t) = 2πf (t) and if it is, what is means, or whether it has any particular application.

Here we have something else again, which looks like an attempt to describe the amplitude and the frequency: I'm looking at PLL's and I see this: A sin (2πf t + θ). It does not read ν = A sin (2πf t + θ), but I guess it could do so. Also it does not read ν (t) = A sin (2πf t + θ). So, what is going on here?

I do seem to understand when there is a situation where an exam-type of question is asked. For instance: Write the expression describing a sinusoidal signal, where the period is 20 Ms, A is 200V and ν is 75V. Okay, so the frequency is 50Hz. So, we get: +75V = 200 sin (100π + 0.375). I got the sine of theta, by dividing 75 (opposite) by 200 (hypotenuse). Of course the answer (+75V) has nothing to do with the frequency part of the equation, I mean, the 100π is ignored in the calculation of the answer. Which to me seems an odd thing. Clearly, this mathematical description is of a signal that is 22.02431 ° from the start of the cycle. That is 0.384 of a radian. So, as I have written it, the worked out equation says nothing, directly, about the phase angle. Or, the point, in terms of phase angle, at which 75V is reached. I'm assuming that + 0.375 is the correct number in the equation, and not 0.384.

I'm not at all sure why someone would devise a way of calculating ν, and half of the equation has nothing to do with the means of calculating that. Of course, A sin (2πf t + θ), which I see when looking at PLL, says nothing explicitly about calculating ν. If fact it does not look like an equation as such.

And finally, I'm not sure what is going on when I see things like: ν (t). Or f (t). Thanks if you can help. Rich

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