Delta-Sigma-Modulator

Delta-Sigma modulator (DSM) for fractional phase locked loop.

File Structure

.
├── HK-MASH-DDSM  # HK-MASH or Traditional-MASH
│   ├── rtl       # verilog
│   └── tb        # testbench
├── SP-MASH-DDSM  # SP-MASH
│   ├── rtl
│   └── tb
├── PSD
│   └── PSD.m     # Calculate the power spectral density
├── LICENSE
└── README.md

Recommended parameter settings

Traditional MASH DSM

top: HK-MASH-DDSM/rtl/hk_mash111.v

parameter	value
WIDTH	9
A_GAIN	0
OUT_REG	1

HK-MASH DSM

top: HK-MASH-DDSM/rtl/hk_mash111.v

parameter	value
WIDTH	9
A_GAIN	2
OUT_REG	1

SP-MASH DSM

top: SP-MASH-DDSM/rtl/sp_mash111.v

parameter	value
WIDTH	9
OUT_REG	1

---

Analysis

Traditional MASH DSM

In HK-MASH-DDSM/rtl/hk_mash111.v, when parameter A_GAIN is set to 0, hk_mash111 works in traditional mode.

When input width(parameter WIDTH in hk_mash111) is set to 24bit(WIDTH = 24) and the input is 0.5(x_i = 2^23), the Power Spectral Density(PSD) of output is shown in the figure below.

HK-MASH DSM

In HK-MASH-DDSM/rtl/hk_mash111.v, when parameter A_GAIN is not equal to 0, hk_mash111 works in HK-MASH mode.

The relationship between coefficient a and parameter A_GAIN in hk_mash111 is shown in the following formula.

a = A_GAIN*2-1

Parameter detail:

parameter	value
WIDTH	24
A_GAIN	2
OUT_REG	0

When input width(parameter WIDTH in hk_mash111) is set to 24bit(WIDTH = 24) and the input is 0.5(x_i = 2^23), the Power Spectral Density(PSD) of output is shown in the figure below.

SP-MASH DSM

When every EFM's input width is set to the same width, this structure operates bad. The following figure is the PSD of output when input is 0.5 of 24bit:

So change the structure like this:

The input width of the first EFM is set to 5bit, other EFM input width is 9bit. Shift e_1 to the left by 4bits as the input of the second stage EFM.

Parameter detail:

parameter	value
WIDTH	9
OUT_REG	0

Power Spectral Density(PSD) of output is shown in the figure below.

Improve

When the DSM of the above three structures is mapped to the circuit, you will find that there is a long logic path collecting all the adders. This can limit the operating frequency of the circuit. A sample way to avoid this is adding registers to cutoff long logic path.

However, if we add one register between two adjacent EFM, it can strengthen the noise at certain frequencies.

PSD of HK-MASH when input is 0.5 of 24bit with one output register:

PSD of SP-MASH when input is 0.5 with one output register:

In order to match the timming of output, we add three registers to the first EFM output, add two registers to second EFM output and add one register to the last EFM output.

HK-MASH DSM 1:

Parameter detail:

parameter	value
WIDTH	24
A_GAIN	2
OUT_REG	1

PSD(input 0.5):

HK-MASH DSM 2:

Parameter detail:

parameter	value
WIDTH	9
A_GAIN	2
OUT_REG	1

PSD(input 0.5):

SP-MASH DSM:

Parameter detail:

parameter	value
WIDTH	9
OUT_REG	1

PSD(input 0.5):