# Tag Info

57

One way would be to describe a sinewave with respect to the unit circle. The radius obviously draws a circle BUT the x and y co-ordinates trace out the familiar waveforms. This also helps with pictorially explaining Eulers formula: $e^{i x} = cos(x)+ i\cdot sin(x)$ where the special case of $x = \pi$ yields Eulers identity: $e^{i \pi} + 1 = 0$ (...

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Circular motion produces a sine wave naturally: - It's just a very natural and fundamental thing to do and trying to produce waveforms that are different is either more complicated or leads to unwanted side effects. Up and down motion (in nature) produces a sine wave against time: -

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Because sinusoids have some important mathemtical properties. The first being how they behave under differentiation and integration. $$\frac{d}{dt}\sin(\omega t+\varphi) = \omega\cos(\omega t+\varphi) = \omega\sin(\omega t+\varphi+\frac{\pi}{2})$$ In other words when we differentiate or integrate a sinusoid we get a sinusoid of the same frequency. The ...

38

The easiest explanation I find is encapsulated in the moving image above. It's all about right angle triangles existing inside a circle. Picture taken from here. See also Why is a sine wave preferred over other waveforms.

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I would try a soundcard. Connect a resistive load (eg. light bulb) to the inverter. Wrap a piece of wire around one of the cables leading to the bulb (DO NOT CONNECT DIRECTLY), connect to mic input and try recording. You should be able to see how (un)clean the power is.

25

The main problem with sine wave generation is that it takes two resonant elements to tango in producing a 180° phase shift -- classically, an inductor and a capacitor. At RF, this isn't a problem -- inductors are easy. However, as you get into lower frequencies, the large inductors involved become unwieldy, which is why alternative sine generation ...

21

Simple: a sine wave in time, t, is the imaginary part of: $$e^{j \omega t}$$ where ω is the angular frequency.

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Cosine and sine waves (actually their constituents in the form of complex exponentials) are the Eigenfunctions of linear, time-invariant systems, having a time-dependent system response of \begin{align}f\bigl(a(t)+b(t),t_0\bigr)&= f\bigl(a(t),t_0\bigr)+f\bigl(b(t),t_0\bigr)&&\text{linearity}\\ f\bigl(a(t+h),t_0\bigr)&=f\bigl(a(t),t_0+h\bigr)... 20 If we apply a sinusoidal signal into a linear time-invariant system (LTI), the output of that system will also be sinusoidal, of same frequency, but possibly different phase and magnitude. If we apply an input that can be described as a sum of sinusoids, output will also be the sum of sinusoids of same frequency, possibly different phase and magnitude. This ... 17 The easiest way to do this would be to use a comparator. Picture taken from linked site All you have to do is set your Vref level to where you want your square wave to trigger. When the sine wave crosses the Vref level, the comparator output will go high. As it approaches it again and goes below the Vref level, the comparator output goes low. You will ... 16 Many problems in physics can be formulated as second order linear differential equations with constant coefficients. For continuous ("harmonic" oscillations) without dampening, the movement can be described simply as a differential equation of a function and its second derivative. Without dampening, with f typically being a function of time, you get ... 15 One way is to find the difference between peak and average of the half-waves. Use a diode full wave bridge to rectify the output of the inverter. Put a 1 MΩ resistor across the output of the full wave bridge. Measure that with a ordinary voltmeter. Now add a 10 nF capacitor across the resistor. This cap should be rated for 1 kV or more. Such caps ... 14 Things oscillate according to sine and cosine. Mechanical, electrical, acoustical, you name it. Hang a mass on a spring and it will bounce up and down at its resonant frequency according to the sine function. An LC circuit will behave the same way, just with currents and voltages instead of velocity and force. A sinewave consists of a single frequency ... 14 A pure sine wave is an useful test signal because it has a special property, it contains only energy at a single frequency, while other waveforms contain energy on multiple frequencies. So depending on what is being tested, a sine wave or other waveforms may be used. With a sine wave generator and a tool that can simply measure amplitude of sine wave (e.g. ... 13 You have created an ideal (infinite bandwidth OPAMP, infinite output voltage etc...) model which is conditionally stable & executed it. look at your y-axis, it has reach 1.5x$10^{59}$ HUGE!. This is what is causing an exception... its run out of resolution to represent this unstable "oscilator" IF a closer to reality OPAMP is used (+-15V, gain ... 12 Easy. Start at steam locomotives. Sine is the position of its piston relative to the angle of the wheel.* You can go look at one in a museum: trig in living color. For instance look at the linkage at 3:00 and 9:00 positions (90 and 270 on the sinewave, where it is flat) and you see where the piston has a problem: it can't apply any force. That's why ... 12 The first waveform looks fine for mains, it can get much worse. I suggest you use a rent a power corruptor, or use a lab with an operator, to see how vulnerable your dimmer is. And work with those results to improve the design of the phase angle dimmer. 11 Is there any other better way to get a pure sine wave from square wave without this voltage drop? Take your square wave and use a phase lock loop to generate a frequency that is maybe 50 times higher: - Then use a clock tunable filter like this: - Feed your square wave at the input (Vin) and you should get a pretty decent looking sinewave at the output. ... 11 "Am I missing something, but it seems that simple electronics are not particularly compatible with sine wave generators?" Let me start my answer with the following sentence: "A good harmonic (linear) oscillator needs a suitable non-linearity" . The reason for this apparent contradiction was explained in another answer already: Each "sinusoidal" oscillator ... 11 Only sine wave don’t have harmonics (frequency spectrum at integer multiples of the main periodic frequency), which have energy, and thus can radiate RF above and outside the fundamental frequency. See “Fourier”. Testing with a non-sinewave also tests at all those harmonic frequencies, which, if not being done intentionally, can end up messing up the test ... 10 It does oscillate, you can see that it does on the right side of the plot. If you zoom in on the left side you should also see the oscillation but at a much smaller amplitude. Your misconception comes from the fact that you first have to understand the theory of operation of oscillators. I suggest reading about the Barkhausen stability criterion. This ... 10 Start with this: simulate this circuit – Schematic created using CircuitLab Say: we have the inductor L1. We charge C1 separately, and then quickly connect it as shown, so that the top side of this circuit is at +1V potential relative to the lower side. Ask yourself (or the student(s)): What will happen next? Clever students will say: yeah, ... 9 On a more mathematical and physical sense why sine and cosine happen to be the fundamentals of waves can have its roots on the Pythagorean theorem and calculus. Pythagorean theorem gave us this gem, with sines and cosines: \mathrm{sin}^2(t) + \mathrm{cos}^2(t) = 1, t \in \mathbb{R}  This made sines and cosines cancel each other out in the inverse-...

9

Scientists did not chose the sine wave, that's what they got from an AC generator. In AC generator, sine wave is generated due to the rotor motion inside a magnetic field. There is no easy way to make it otherwise. See this figure in Wikipedia. http://en.wikipedia.org/wiki/Single-phase_generator#Revolving_armature

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I would like to suggest that the comparator circuit shown by @hwengmgr could use some small improvements over what was posted. Improvements include: Bigger capacitor value to reduce filter effect of the capacitor at frequency. Larger value resistors in dividers to reduce current load on source supply. Added hysteresis at the comparator to make the circuit ...

8

With a high fps camera set to manual exposure, a big resistor (>~10k), and a couple of scrap LEDs (not white) back-to-back in parallel you should be able to measure the brightness -- does it change smoothly or in steps? But you are working with mains if you build something like that, even if it is isolated from ground. How easy it is to read the brightness ...

7

One way is to use a peak detector, but this has a diode voltage drop, which gives an error in the result. You don't say anything about frequency, but I'll assume it is much lower than the ADC's sampling frequency. I would use a resistive voltage adder to bring the full signal within the ADC's range. The resistive adder has the advantage over the ...

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In the specific example you gave, the square wave is much louder; mostly for physiological reasons. 1) Into the same load, a square wave will deliver twice the power as a sine wave of the same peak voltage. This is same as saying the square wave has an RMS voltage equal to its peak value; whereas a sinewave has an RMS value of 0.707 (actually sqrt(2)/2) ...

7

Your friend, the Wien-Bridge oscillator. Uses just opamps and resistors/capacitors. produces very clean sine waves in the low frequency range. There are many variations, with C=C1=C2, R = R1=R2, it oscillates at $f = \frac{1}{2\pi RC}$. Rb is a lamp used for temperature Compensation, although there are many variations don't require it, for instance, using ...

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