# What is Numerically Controlled Oscillator (NCO) ?

It is a digital signal processing component that generates a periodic waveform, typically a sine wave, with a frequency that can be precisely controlled through numerical values. Unlike traditional analog oscillators, NCOs operate in the digital domain and are commonly used in various applications such as digital signal processing (DSP), software-defined radios, frequency synthesis, and communications systems.

The key feature of an NCO is its ability to generate an output waveform at a frequency determined by a numerical input, often referred to as the phase increment or tuning word. By updating this numerical value, the frequency of the output waveform can be changed dynamically and precisely. This makes NCOs valuable in applications where frequency agility, accuracy, and rapid frequency changes are essential.

## Working of NCO

The working principle of a Numerically Controlled Oscillator (NCO) involves the generation of a periodic waveform, often a sine wave, through digital means. The key element is the concept of phase accumulation. NCO is the part or component of the DDS based synthesizer. The NCO consists of two parts viz. phase accumulator and phase to amplitude converter as shown in the figure below. The output of NCO is given to Digital to Analog Converter (DAC). The popular IC which houses NCO built-in is DDS AD9851 from Analog Devices.

➨The basic principle of an NCO involves accumulating phase increments over time and using the
accumulated phase to determine the output waveform.

➨The phase increments are proportional to the desired frequency, and the rate at which they are
accumulated controls the frequency of the generated waveform.

➨By updating the tuning word, the frequency can be dynamically changed.
The digital nature of this process allows for precise control and manipulation.

The software algorithm or program for NCO can be summarized in the following steps.

Step-1 (Initialization) : Start with an initial phase value.

Step-2 (Accumulation): In each time step or clock cycle, add a phase increment to the current phase value.

Step-3 (Waveform Generation): The accumulated phase is used as an index to lookup or compute the value of
the waveform at that specific phase, creating the output signal.

The mathematical equation for the output frequency (F_{out}) of a DDS synthesizer as a function of
tuning word 'M' is given by following equation.

➨ F_{out} = [ (M * F_{clk}) / 2^{n} ]

Where,

F_{out} = Output frequency

M = Tuning Word

F_{clk} = Clock frequency of NCO

n = Bit width of tuning word (i.e. number of bits used to represent the tuning word)

The phase increment, often called the tuning word, determines the frequency of the generated waveform. By updating the tuning word, the frequency can be dynamically changed. The digital nature of this process allows for precise control and manipulation.

Example calculation :

INPUT : Tuning word = 1000, Clock frequency = 10 MHz, Bit width = 12 bits

OUTPUT : DDS synthesizer output frequency = 2441.41Hz

## Advantages of NCO (Numerically Controlled Oscillator)

Following are the benefits or advantages of NCO.

1. Precision : NCOs offer high frequency resolution and precision due to their digital nature. The tuning word can be adjusted with fine granularity, enabling accurate frequency control.

2. Flexibility : NCOs are versatile and can generate various waveforms, not just sine waves.

3. Frequency Agility : Rapid and dynamic changes in frequency are easily achievable with NCOs, making them suitable for applications requiring agile frequency synthesis.

4. Integration : NCOs can be seamlessly integrated into digital signal processing systems, facilitating digital communication and signal processing tasks.

5. Low phase noise : Compared to some analog oscillators, NCOs can exhibit lower phase noise, which is crucial in applications like communication systems where signal quality is paramount.

## Applications of NCO

Following are the common applications of NCO.

• NCOs play a crucial role in Software-Defined Radios (SDRs), enabling the flexible generation of signals with programmable frequencies for communication purposes.

• NCOs are used in frequency synthesizers to generate stable and accurate signals for various applications, such as in RF (radio frequency) transceiver systems.

• NCOs are fundamental in Digital Signal Processing (DSP) applications for tasks like modulation, demodulation, and filtering.

• Test and Measurement (T & M) instruments like signal generators and arbitrary waveform generators use NCOs for precise waveform generation.

• NCOs are employed in radar systems for generating and processing signals with specific frequencies and waveforms.

• In applications like sonar systems, NCOs are used for signal generation and processing in underwater acoustic environments.

**Conclusion** : In summary, Numerically Controlled Oscillators (NCOs) provide a digital and flexible
approach to waveform generation, offering precision, frequency agility, and versatility in various
applications related to communication, signal processing, and instrumentation.