1. Solutions to Sinc Rolloff Problem
Dr. Hossein Shamsi
K.N. Toosi University of Technology

2. Sinc Rolloff Problem in DACs
The DAC's frequency response is not flat and attenuates the analog output at higher frequencies
E.g. 2.42dB of attenuation at 80% of fs/2
0.1dB frequency flatness is about 0.17 fs/2
That loss is unacceptable for some broadband applications
The output frequency response for most DACs, however, rolls off according to the sin(x)/x (Sinc) frequency-response envelope
However, several techniques are available for coping with the non-flat frequency response of a DAC
Roll off: غلتیدن به سمت پایین
Cope: to deal with and attempt to overcome problems
Maxim

3. Solutions to Sinc Rolloff Problem
Oversampling (Increasing the Update Rate)
Interpolating
Pre-Equalizing
Post-Equalizing
Maxim

4. Solutions to Sinc Rolloff Problem
Oversampling
In a ZOH DAC the envelope of the output spectrum is
identical to
By oversampling we can mitigate the sinc roll-off problem.
Disadvantages:
More speed (cost)
More power consumption
Envelope: پوش
Mitigate: کاهش دادن
Maxim

5. Solutions to Sinc Rolloff Problem
Interpolating
This technique increases the update rate while keeping the data rate at a lower frequency
Interpolation DACs include one or more digital filters
E.g. MAX5856 incorporates two interpolation stages to achieve an 4x interpolation(the DAC's update rate is four times the data rate)
Maxim
Incorporate: یکپارچه کردن، ضمیمه کردن

6. Interpolating
Maxim

7. Functional Block Diagram
Maxim

8. MAX5856A
Maxim

9. Solutions to Sinc Rolloff Problem
Pre-Equalizing
Increasing the update rate reduces but does not eliminate the effect of Sinc rolloff
A digital filter whose frequency response is the inverse of the Sinc function, just before feeding the DAC.
Maxim
Equalizer:همسان ساز

10. Pre-Equalizing Pre-Equalizing An example
The FIR filter designed in the following figure equalizes the DAC's Sinc response and achieves 0.1dB flatness up to 96% of fs/2
Maxim

11. Interpolating and Pre-Equalizing
Maxim

12. Functional Block Diagram
Maxim

13. DAC3484 Application: Cellular Base Stations Diversity transmit
Wideband communication
Maxim

14. Solutions to Sinc Rolloff Problem
Post-Equalizing
An analog filter whose frequency response is approximately equal to the inverse of the Sinc function
This type of analog filters is common to equalize transmission lines and amplifiers
The regarding filter is replaced just after the DAC’s lowpass reconstruction filter
Maxim

15. Solutions to Sinc Rolloff Problem
Post-Equalizing
An example
This simple active equalizer increases 0.1dB flatness from 17% to 50% of fs/2
Maxim

16. Reconstruction Filter
Also called smoothing filter
Same situation as with anti-aliasing filter for ADCs
A brick wall filter would be nice
Oversampling helps reduce filter order
Murmann