Sinc Filter Design for sigma delta ADC

Papabravo

Joined Feb 24, 2006
21,225
Thanks for the quick response ; how do i design it using digital circuits
What does the algorithm given in the chapter suggest?
My answer would be: "that algorithm suggests the use of a digital signal processor". If you don't like that suggestion, then I would suggest using an FPGA to implement the algorithm with the requisite MAC (Multiply Accumulate) architecture. Would that be within your capabilities?
 

Papabravo

Joined Feb 24, 2006
21,225
You give us a sketch with no part numbers or component values and make a claim about the behavior with no indication what your criteria are. I can't figure out what you are going on about.
 

Thread Starter

Raj_Singh

Joined Nov 26, 2023
31
You give us a sketch with no part numbers or component values and make a claim about the behavior with no indication what your criteria are. I can't figure out what you are going on about.
The opamps are at transistor level and not an IC from the market
The resistor and capacitor values are 35kohm and 150pf
 

Papabravo

Joined Feb 24, 2006
21,225
The opamps are at transistor level and not an IC from the market
The resistor and capacitor values are 35kohm and 150pf
What software did you use to create the plot, and what does the plot purport to show? It looks like a low pass filter converting a PWM into a sine wave. Stringing two first order low-pass sections together does not necessarily make a 2nd order section. It is essentially creating a double pole at the corner frequency. A true 2nd order section would create a complex conjugate pair with the appropriate corner frequency and Q.

For example, a 2nd order Butterworth filter would have a normalized transfer function that looks like:

\( T(s)\;=\;\cfrac{\omega_0^2}{s^2+(\omega_0 /Q)s+\omega_0^2} \)

\( \text{where }\omega_0\text{ is the corner frequency, and }Q\text{ defines the angle the poles make with the negative real axis.} \)

To normalize the equation so the DC gain is unity, or 0 dB, divide numerator and denominator by \( (\omega_{0})^2 \), then you would have:

\( \cfrac{1}{\left(\cfrac{s}{\omega_{0}} \right)^2+\left(\cfrac{1}{\omega_0Q}\right)s+1} \)

\( \omega_0\text{ is in radians/sec, and }Q\;=\;{1}/{\sqrt{2}}\;\approx\;0.707 \)
 
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Papabravo

Joined Feb 24, 2006
21,225
Here is an example of a 2nd order Salen-Key filter using a unity gain opamp.

1702577395720.png
The corner frequency is computed as follows for some standard resistor values:

\( f_{c}\;=\;\cfrac{1}{2\pi\sqrt{2}\cdot C1\cdot RK} \)

\( (2\pi\sqrt{2}\cdot(0.01\text{ }\mu\text{F})(562\text{ }\Omega))^{-1}\approx 20.02\text{ kHz} \)
 
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