Multibit DAC

Below is a 8 bit R2R DAC circuit that I built for use with my Parallax chips. Its intent is to be cascaded with the analog out of one feeding the analog reference (AIN) of the second DAC. By feeding the DAC's with a bitpattern incrementing to a peak the decrementing to a min and incrementing back up the DAC will produce a symmetrical ramp. This ramp when provided to the second stage will linearly modify the conversion ratio of the second DAC such that if its bitpattern matches the period and waveshape of the first and is time shifted 90 degrees to the first, as symmetrical sinewave is the result. Mathmatically the derivative of a sine is a symmetrical ramp, if a further derivative is applied , a Square wave of 50% duty cycle is the result. In out beloved Mega chips there is a similar circuit whose analog output is compared to the selected analog pin, the bits driving the DAC come from a ripple carry counter. When the comparison of the 2 signals changes from low meaning the analog pin's voltage is greater than or equal to the DAC, the ADC signals "Conversion complete" and the current count of the Ripple counter is latched and made ready for retrieval by the Mega's databuss.

I can provide you with the board layout on a request basis. The board was created in WinBoard 2.4 and I doubt may of you have the WinDraft/WinBoard suite.

Mathmatically the derivative of a sine is a symmetrical ramp

It's quite a long time since I did calculus but I don't think it's changed that much. The derivative of the sin function is the cosine function and the derivative of cos is -sin.

Pete

The integral of sine is cosine. The derivative is a measure of the slope.

Pete check your circuit description of differentiator and integrator.

ajofscott: The integral of sine is cosine. The derivative is a measure of the slope.

The derivative is the instantaneous slope. The way the slope of sin(x) changes with respect to x is exactly cos(x).

The integral is the area under the curve. The way the area under sin(x) changes with respect to x is exactly -cos(x).

Pete check your circuit description of differentiator and integrator

What circuit? I don't need no steenkin circuit. It is a mathematical fact that the derivative of sin is cos and the derivative of cos is -sin. And, furthermore, that the integral of sin is -cos.

Pete

Verdris:

ajofscott: The integral of sine is cosine. The derivative is a measure of the slope.

The derivative is the instantaneous slope. The way the slope of sin(x) changes with respect to x is exactly cos(x).

The integral is the area under the curve. The way the area under sin(x) changes with respect to x is exactly -cos(x).

Pedanty: the intricacies of calculus are there because the instantaneous slope is not defined or meaningful.

because the instantaneous slope is not defined

If the instantaneous slope is not defined then the derivative is not possible. A function such as sine is continuous everywhere and therefore it is differentiable everywhere which means you can find the slope of the curve at any point. However, there are many functions which have discontinuities which make them non-differentiable at some points - the tangent function for example. In a calculus course you also run into pathalogical functions which can't be differentiated at all. e.g. the function "y=x where is x is any integer" cannot be differentiated anywhere.

Pete

Boy! I did not intend to start a war!

I just mean that an instantaneous part of a curve is just a single point, its not unique to any one curve and it doesn't have a slope. A derivative is a property of the function. The instantaneous value of a derivative is by convention thought of as the slope of the curve at that point, but specifically its of the curve, not the point.

Nobody said a point has a slope. The derivative (if it exists) of a function at a given point is the slope of the tangent to the curve at that point - its not a convention. e.g. for y=sin(x) the derivative of y is given by y'=cos(x) and the slope of y at x=0 is 1 - i.e. y'(0)=cos(0)=1 which means the slope of the sin function at x=0 is 1.

Pete P.S. It isn't a war - just a misunderstanding (I think)

Yes, I take words like "instantaneous" literally ;)