Question E7H09:
What type of frequency synthesizer circuit uses a phase accumulator, lookup table, digital-to-analog converter, and a low-pass anti-alias filter?  

Choices:  
A: A direct digital synthesizer  
B: A hybrid synthesizer  
C: A phase-locked loop synthesizer  
D: A direct conversion synthesizer    

Correct Answer is  A: A direct digital synthesizer  

Correct answer: A — A direct digital synthesizer (DDS)

1) Why A is correct
- A DDS generates a waveform numerically:
  - Phase accumulator: adds a frequency control word each clock, producing a running phase.
  - Lookup table: maps phase to sine amplitude.
  - DAC: converts samples to analog.
  - Low-pass (reconstruction/anti-alias) filter: removes images from the DAC’s stepped output.
- Key formulas:
  - Let the clock be $f_{clk}$, accumulator width $N$ bits, and frequency control word $K$.
  - Output frequency: $$f_{out} = \frac{K}{2^N}\,f_{clk}$$
  - Frequency resolution: $$\Delta f = \frac{f_{clk}}{2^N}$$
- Rule of thumb: “Phase accumulator + LUT + DAC + LPF” uniquely identifies a DDS.

2) Why the others are incorrect
- B: Hybrid synthesizer
  - Combines two methods (often DDS driving a PLL) to get low phase noise and fine resolution. It is not just a DDS core alone; it adds PLL/VCO blocks not listed in the question.
- C: Phase-locked loop (PLL) synthesizer
  - Uses a phase detector/charge pump, loop filter, VCO, and dividers. It does not use a phase accumulator, LUT, and DAC as its core elements.
- D: Direct conversion synthesizer
  - “Direct conversion” typically describes a receiver architecture (RF to baseband in one mix), not a frequency synthesizer using phase accumulators and LUTs.

3) Useful rules of thumb
- DDS spur/images occur at $k f_{clk} \pm f_{out}$; the LPF passband should cover $f_{out}$ and reject images near $f_{clk}$.
- For finer frequency steps, increase $N$ or decrease $f_{clk}$. For wider tuning range, increase $f_{clk}$.