A 16bit D/A interface with Sinc approximated semidigital reconstruction filter
7.4. Semidigital FIR filter principles
Consider fig.7.6 where the basic principle of the current driven D/A interface is shown [11]. As explained in section 6.2, it consists of a FIR semidigital filter with 1
Fig.7.6: Basic principles 
bit digital delay units and analog tap weights followed by an analog postfilter [14]. The input of the D/A interface is a bitstream signal already noiseshaped. The current source I_{0} needed to prescribe the common mode level at the input introduces noise. Integrating on the same chip analog and digital circuits, the substrate noise can become a problem in the single ended approach.
That is why we have introduced the differential D/A from fig.7.7. The 1bit output of the noiseshaper with a sample frequency of 2.8MHz will pass through the 1bit digital delay units implemented with shiftregisters. The outputs of the shift registers are controlling the switches of the current taps directing the current to the negative or positive input of the opamp. The noiseshaper and the upsampling filter are not integrated on the same chip. The FIR filter has unity transfer for the baseband signal, with minimum ripple and attenuates the outofband quantization noise. Due to oversampling, the analog postfilter can be simply reduced to a first order filter thus simplifying the integration onchip of the digital and analog functions.
The coefficients of the filter implemented with weighted current sources, have the property that a_{k}=a_{Nk+1}. The filter is symmetrical with respect to the middle coefficient. Due to the differential approach if a current DI is flowing towards the positive input of the opamp, a negative current DI is flowing towards the negative input of the opamp. Therefore, the current is not being dumped to ground as will be in the case of singleended solutions [see fig.7.6]. The differential approach has been used to make larger voltage swings at the output. The effect of digital crosstalk and the glitches in the output current will be minimized. Given the data x[n] at the input of the shift registers, the currents at the input of the opamp are:
(7.9)
(7.10)
Fig.7.7: Basic principles 
The filter coefficients are implemented by using current sources with different weights a_{k} The output of the shiftregisters is time continuous due to the holding property. During sampling interval, the current is delivered continuously to the output of the FIR and therefore zeroorder hold effect is being encountered. The analog continuoustime first order RC filter attenuates further the ripple present in the output of the FIR filter. Given the pole of the lowpass filter f_{p} and the sampling frequency f_{s} the total transfer function of the FIR and continuous time analog filter including the zeroorder hold effect will be:
(7.11)
The total transfer is considered when the coefficients of the filter are being calculated. The cutoff frequency of the lowpass filter should be chosen such that the passband response is not impaired.
