dc-offsetmicrocontrollerwave
I have a wave profile stored in a micro-controller that I want to scale and shift with two input arguments. Is it possible to fix an 'absolute' scale (max/min = 1.02 for e.g.) and have an offset that is unchanged? Currently I can add the offset first, account for the scale inherent in the wave and scale it again to get my desired scale, but this changes the offset.
Is there a way to do this?
What you need to do is simply remove the DC offset all together, not supply a negative one. This is known as AC coupling. If you run the output of your square wave generator through series capacitor, it should do what you need. This will however be at the expense of making the square wave less square.
An example circuit is shown below for you:
And the output would look like this (Green Trace = Generator Output, Blue Trace = Voltage Across Resistor):
You will probably get a little voltage loss (meaning your peaks will be a little less that +/- 2.5V) since no capacitor is ideal, but you can get a pretty good square wave output if you get the right value capacitor. You'll have to experiment and see. Usually, the larger capacitor value you choose, the closer your output waveform will be to the original for any frequency a benchtop square wave generator is outputting.
Your block daigram shows no relationship between the Oscillator/Divider and the Waveform generator, but these must be optimized for synchronous mixing.
Can you try a simple approach?
To mix the the sine input and output, may I suggest the classic 180deg range XOR mixer which is commonly known as a Type I PLL phase detector. The inputs are the same frequency and the output is the difference phase and sum frequency ( + harmonics) so a LPF must be chosen to easily suppress the 2f components yet provide fast tracking of phase vs voltage.
let R1C1 = R2C2 = R3/C3 = 1000/f = 1000/250KHz = 4ms
let R1 = 1~10 MΩ, Let R3 ~ 1KΩ to drive ADC
use buffered inverters '04 and '86 XOR
Average ADC readings to achieve desired resolution and noise reduction by √n samples.
Best Answer
Let me see if I understood this properly:
Your constraints are a given offset and max/min ratio, and your wave has some original minimum (m) and maximum (M) values, that you wish you scale+offset in order to meet the constraints.
If that is the case then you can simply scale with respect to the minimum and then offset.
Any point in your wave will be scaled with respect to the minimum and offset:
$$ y=scale\cdot (x-m)+m+offset $$
The offset is given, you just need the scale:
$$ ratio = \frac{max}{min} = \frac{scale\cdot (M-m)+m+offset}{scale\cdot (m-m)+m+offset} $$
You just need to solve for scale in the above equation.
Another method would be to scale with respect to zero or mid-range, and then apply the offset. I'm just not sure what your application requires.
If you scale with respect to zero, then the above equations get reduced to:
$$ y=scale\cdot x+offset $$ $$ ratio = \frac{max}{min} = \frac{scale\cdot M+offset}{scale\cdot m+offset} $$