# Fractional Clock Divider with DSM

Delta Sigma Modulator based fractional clock divider

**Library:**Mixed-Signal Blockset / PLL / Building Blocks

## Description

Using delta sigma (Δ-Σ) modulation technique, a Fractional Clock Divider with
DSM reduces the primary fractional spurs by spreading out the range over
which the **div-by** value is varied. This block allows delta sigma
modulation of up to 4th order.

## Ports

### Input

`clk in`

— Input clock frequency

scalar

Input clock frequency that needs to be divided, specified as a
scalar. In a phase-locked loop (PLL) system, the **clk
in** port is connected to the output of a VCO block.

**Data Types: **`double`

`div-by`

— Ratio of output to input clock frequency

fractional scalar

Ratio of output to input clock frequency, specified as a fractional
scalar. The value at the **div-by** port,
*N.FF*, is split into two parts: the integer part
(*N*) and the fractional part
(*.FF*).

For an *n*th-order delta sigma modulator, the value
at the **div-by** port is achieved by varying
*N* between 2^{n} different
integer values.

**Note**

For an *n*th order delta sigma modulator, use a
value ≥ 2^{n} at the **div-by** port.

**Data Types: **`double`

### Output

`clk out`

— Output clock frequency

scalar

Output clock frequency, specified as a scalar. In a PLL system, the
**clk out** port is connected to the feedback input
port of a PFD block. The output at the **clk out**
port is a square pulse train of 1 V amplitude.

**Data Types: **`double`

## Parameters

`Delta Sigma Modulator order`

— Order of the Delta Sigma Modulator

`3rd order`

(default) | `1st order`

| `2nd order`

| `4th order`

The order of the delta sigma modulator.

For an *n*th-order of the delta sigma modulator, the
value at the **div-by** port is achieved by varying the
*N* counter value between 2^{n}
different values. Modulator order defines the range of values by which the
signal at the **clk in** port will be divided, providing a
division effect similar to *N.FF* value at the
**div-by** port.

#### Programmatic Use

Use

`get_param(gcb,'dsm')`

to view the current**Delta Sigma Modulator order**.Use

`set_param(gcb,'dsm',value)`

to set**Delta Sigma Modulator order**to a specific value.

`Enable increased buffer size`

— Enable increased buffer size

off (default) | on

Select to enable increased buffer size during simulation. This increases the buffer size of the Logic Decision inside the Fractional Clock Divider with DSM block. By default, this option is deselected.

`Buffer size`

— Number of samples of the input buffering available during simulation

`1`

(default) | positive integer scalar

Number of samples of the input buffering available during simulation, specified as a positive integer scalar. This sets the buffer size of the Logic Decision inside the Fractional Clock Divider with DSM block.

Selecting different simulation solver or sampling strategies can change
the number of input samples needed to produce an accurate output sample. Set
the **Buffer size** to a large enough value so that the
input buffer contains all the input samples required.

#### Dependencies

This parameter is only available when **Enable increased
buffer size** option is selected in the Block Parameters
dialog box.

#### Programmatic Use

Use

`get_param(gcb,'NBuffer')`

to view the current value of**Buffer size**.Use

`set_param(gcb,'NBuffer',value)`

to set**Buffer size**to a specific value.

## More About

### Inside the Mask

The Fractional Clock Divider with DSM subsystem
block consists of four delta sigma modulators of orders one to four encapsulated
inside the DSM Selector variant subsystem. The output of the DSM selector drives a
Single Modulus
Prescaler block. Given the **Delta Sigma Modulator
order**, corresponding delta sigma modulator gets activated.

The modulator order defines the range over which the *N* counter
value is varied. For an *n*th-order delta sigma modulator,
*N* is varied over 2^{n} different
values. This variation is achieved by integrating the changes in the fractional part
(*.FF*) from the previous cycle and quantizing the differential
changes.

The general form of the transfer function for an nth order delta sigma modulator is:

$$Y(z)=X(z)+E(z)\xb7{(1-{z}^{-1})}^{\text{n}}$$

where

*Y(z)*= Output of the modulator*X(z)*= Input the modulator*E(z)*= Quantization error

*E(z)* is calculated by subtracting the value of input
*X(z)* in the present cycle from its value in the previous
cycle. In other words, *E(z)* is a form of a digital highpass
filtering.

The higher-order modulators reduce the primary fractional spurs by alternating
*N* over a larger range of integer values. As a result, the
fractional spurs are pushed to higher frequencies in the frequency spectrum and can
be filtered more effectively by the loop filter in a PLL system.

For example, if the third-order delta sigma modulator is activated,
*N* is varied over 8 different values, which can range from
(*N*-3) to (*N*+4).

**Delta Sigma Modulator Sequence**

Modulator Order | Range | DSM Sequence |

1st | 0, 1 | N, N+1 |

2nd | -1, 0, 1, 2 | N-1, N,
N+1, N+2 |

3rd | -3, -2, -1, 0, 1, 2, 3, 4 | N-3, N-2, …,
N+4 |

4th | -7, -6, …, 7, 8 | N-7, N-6, …,
N+8 |

## References

[1] Miller, B. and Conley, R.J.,
*A Multiple Modulator Fractional Divider*. IEEE Transactions on
Instrumentation and Measurement, vol. 40, no. 3, 1991, pp. 578-583.

## See Also

PFD | VCO | Fractional Clock Divider with Accumulator | Single Modulus Prescaler | Dual Modulus Prescaler

**Introduced in R2019a**

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