# Structure of All-Digital Frequency Synthesiser for IoT and IoV Applications
## 3 Requirements for Blocks of All-Digital Multiband Frequency Synthesiser
Also, from the technical documentation of some of most the advanced multiband transceivers presently available [5; 6; 7; 8], it is seen that in-band phase noise should be better than \(-90\) dBc/Hz and out-of-band phase noise should be better than \(-120\) dBc/Hz. From Equation (1) it is seen that noise induced by TDC depends on the resolution of TDC, operating frequency of DCO and frequency of the reference signal. It deteriorates with a higher frequency of DCO, therefore, for theoretical calculations, the highest needed frequency should be used,i.e., 6 GHz. Calculated noise, induced by TDC, when frequency of digitally controlled oscillator is 6 GHz, frequency of reference signal ranges from 10 MHz to 100 MHz and resolution of TDC ranges from 2 ps to 50 ps is shown in Figure 3. As can be seen, the resolution of TDC has to be better than 12 ps to satisfy the in-band noise requirement of \(-90\) dBc/Hz. If resolution of TDC is 4 ps, a better than \(-100\) dBc/Hz in-band noise can be achieved. Oscillator's component of the DCO's noise depends on properties of the resonant tank. Usually LC tank oscillators are used to achieve low phase noise. LC tank DCOs and the oscillator's component of DCO noise are widely researched and discussed [18; 19; 20], therefore, here the focus will be on the quantization component of DCO noise. Figure 4 shows DCO's quantization and \(\Delta\Sigma\) shaping noise and its components, which are calculated by using Equation (3). The following parameters were used: DCO's frequency \(f_{\mathrm{DCO}}\) is equal to 6 GHz, frequency of reference signal \(f_{\mathrm{REF}}\) is 40 MHz, \(\Delta\Sigma\) dithering frequency \(f_{\Delta\Sigma}\) is equal to divided-by-4 DCO's frequency, DCO's frequency tuning step \(\Delta f_{\mathrm{RES}}\) is 50 kHz, \(\Delta\Sigma\) modulator controls 8 bits and order of \(\Delta\Sigma\) modulator is 3. Total DCO's quantization and \(\Delta\Sigma\) shaping noise is marked as \(\mathcal{L}_{\Delta\Sigma}(f)\), DCO's quantization noise without \(\Delta\Sigma\) modulator is marked as \(\mathcal{L}_{\mathrm{q}}(f)\), DCO's quantization noise with \(\Delta\Sigma\) modulator is marked as \(\mathcal{L}_{\Delta\Sigma_{\mathrm{q}}}(f)\), and \(\Delta\Sigma\) noise shaping component is marked as \(\mathcal{L}_{\Delta\Sigma_{\mathrm{q}}}(f)\). Figure 3: Calculated phase noise induced by time to digital converter, when frequency of digitally controlled oscillator’s output signal is 6 GHz, frequency of reference signal is 10–100 MHz, resolution of time to digital converter is 2–50 ps. It can be seen from Figure 4 that \(\Delta\Sigma\) quantization and noise shaping improves DCO's quantization noise by more than 40 dBc/Hz at small frequency offsets from the carrier (in-band). In this range, according to Equation (3), noise depends on the frequency of the reference signal and \(\Delta f_{\mathrm{RES}}/2^{\mathrm{W}}\) ratio. This ratio shows that increasing the \(\Delta\Sigma\) modulator's bit count by one bit corresponds to reduction of frequency tuning step by half. In-band DCO's quantization noise will not be filtered by the synthesiser, therefore it should not exceed the noise induced by TDC. In order for DCO's quantization noise to not exceed \(-100\) dBc/Hz, when frequency of reference signal is 40 MHz, ratio of \(\Delta f_{\mathrm{RES}}/2^{\mathrm{W}}\) should not exceed 2190 Hz, i.e., equivalent frequency tuning step after \(\Delta\Sigma\) quantization should not exceed this value. Such a case, when the raw frequency tuning step (without \(\Delta\Sigma\) dithering) is increased to 560.64 kHz and all other parameters are the same as in previous case, is shown in Figure 5. But it should be noted, that even in sub-micron technologies, a frequency tuning step close to 10 kHz is achievable [14; 21; 22; 23]. Therefore, the requirement of \(\Delta f_{\mathrm{RES}}/2^{\mathrm{W}}\) ratio is relatively easy to meet. \(\Delta\Sigma\) shaping noise dominates at high frequency offset from the carrier (out-of-band).