Three-Points Modulator Based on DPLL for Wideband Polar Modulation

doi:10.4236/cn.2013.53B2027

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Communications and Network, 2013, 5, 140-143

http://dx.doi.org/10.4236/cn.2013.53B2027 Published Online September 2013 (http://www.scirp.org/journal/cn)

Three-Points Modulator Based on DPLL for Wideband

Polar Modulation

Julien Kieffer1, Sébastien Rieubon1, Marc Houdebine2, Sébastien Dedieu2, Emil Novakov3

1ST-Ericsson, Grenoble, France

2STMicroelectronics, Crolles, France

3IMEP-LAHC, University of Grenoble-Alpes, Grenoble, France

Email: [email protected]

Received May, 2013

ABSTRACT

We present a nonlinear event-driven model of a Digital PLL used in the context of a polar modulation. This modeling

has shown that the estimation method of the TDC gain has a big impact on the EVM for wideband modulation and a

solution has been proposed which consists to add the modulation on the gain after calibration of the gain offset. This

transforms the classical two-points modulator into a three-points modulator. This implementation has been validated for

WCDMA standard.

Keywords: DPLL; Polar Modulation; WCDMA; TDC

1. Introduction

The number of wireless standards has expanded during

the last decade, allowing the use of new applications

such as internet for mobile or video calls for example.

These new functions are very demanding in terms of de-

bit rate. New communications standards have been de-

veloped to follow this evolution such as WCDMA and

LTE for mobile phone. Their requirements in terms of

noises, spurious, consumption, etc. are more and more

stringent and their bandwidths more and more wider. In

this context, the polar transmitter as shown in Figure 1

seems to be an attractive architecture to reach these tough

specifications.

The typical IQ signal, produced by the modulator, is

converted by a Coordinate Rotation Digital Computer

(CORDIC) into a polar signal. Lots of studies of the am-

plitude modulation by the Power Amplifier (PA) can be

found in the literature[1,2], but the phase modulation by

the PLL, which could be either analog or digital, seems

to be less studied, especially for wideband modulations.

This will be the core of this work.

In order to study the phase path, the modeling of the

PLL has to be even more and more accurate. Many fre-

ency-domain models have been developed in the past

years from the classic Laplace model which can be used

to study transfer functions and PLL noises to more com-

plex sampled models [3-5] which are now very useful for

the study of polar modulation. The model of Digital PLL

proposed in this paper allows even more precision in the

modeling of the different blocks of the PLL by including

noises and nonlinearities and still allows fast simulation

because it is event driven.

As already said, the main application for which our

model has been developed is to observe the impact of a

modulation passing directly through the PLL in the case

of a polar modulation.

e-point modulator can be used for narrowband modu-

lations, where the bandwidth is lower than the PLL

cut-off frequency. The modulation is transmitted by add-

ing the modulation data to the PLL frequency command

word. Meanwhile, modulation bandwidth can be slightly

enlarged by using a pre-distortion filter which compen-

sates the PLL low path filtering [8]. However, PLL fil-

tering and pre-distortion transfer function fitting mis-

matches limit the modulation bandwidth extension. Sev-

eral methods for reducing the modulation bandwidth

have also been proposed.

Figure 1. Polar transmitter.

J. KIEFFER ET AL. 141

On thus, for wideband modulations, two-point modu-

lator [9] is necessary in order to release constraints due to

PLL bandwidth and to remove pre-distortion filter. To go

beyond PLL low path filtering, the modulation can be

sent directly to the PLL output. Meanwhile, the modula-

tion still has to be added to the PLL control word to

avoid the loop feedback high pass filtering. This two

point modulation reduces the impact of the PLL cutoff

frequency on the modulation bandwidth.

This paper describes the proposed Digital PLL archi-

tecture model which underlines the necessity of 3 point

modulation.

2. Digital PLL Time-Model

A simplified block diagram of a DPLL [6] on which our

model is based is shown on Figure 2.

The PLL output frequency is defined by









mod

().

dco ref

iNff fi  (1)

where N and f are respectively the integer and the frac-

tional part of the division ratio between the output fre-

quency corresponding to the addressed channel and the

reference frequencyfref and fmod the eventual modulation

frequency.

fdco is generated by a Digitally Controlled Oscillator

(DCO) from a command word (Cmd). A Frequency-

Meter (FM) allows the conversion from the analog to the

digital world, where the comparison between the wanted

word, N+f, and the measured word, N+f|m is made. The

intensive digital architecture allows the implementation

of a digital loop filter.

Firstly, the model is described with the PLL used at

first only as a frequency synthesizer.

2.1. Model Explanation

The proposed time-model is event-driven. Its efficiency

comes by the limited number of calculation points, which

allows reducing the simulation duration and the size of

the database. So it simplifies the FFT for the phase noise

analysis. Thus, the computations are done only for the

useful edges: at least reference and DCO edges as shown

on the chronogram on Figure 3.This allows fast simula-

tions (about 50 μs/s of simulation in Matlab).

The chronogram describes the succession of phase

displacement ∆t which is related to the fractional part of

Figure 2. Three-points modulator based on digital PLL.

the frequency ratio. The main equation governing the

PLL behavioris:

















1cpt dcoref

titiNiTiT  (2)

where Ncpt is the number of DCO periods between two

rising edges of the reference which is given by a counter.

The fractional residue ∆t is measured by a Time to Digi-

tal Converter (TDC).

2.1.1. TDC

In reality, the delay between the reference edge and the

following DCO edge is quantized by a TDCif a precision

better than more or less half a period of DCO is re-

quired.Several types of TDC exist in the literature; each

one of them presents nonlinearities due to the analog-

to-digital conversion. This represents the strongest non-

linearity in the loop. The TDC outputs two digital words

corresponding to the phase displacement and the number

kof quantization steps Tqover a DCO period as shown on

Figure 4.

The digitized phase displacement can here be modele-

das the integer part of the following ratio:

 



Mi T



 (3)

Then, the equation (2) is replaced by:



















refcpt dcoq

TNiTiMiMiT (4)

An estimation of the TDC gain, here called k, is re-

quiredto get back to the Tref/Tdco frequency ratio.

 



dco

ki T

 (5)

This measurement method is impacted by a quantiza-

tion error so that a better precision can be achieved by

filtering. Finally, equation (4) can be rewritten and gives

the digital word corresponding to the frequency ratio:

Figure 3. Chronogram.

Figure 4. TDC inputs/output s.

J. KIEFFER ET AL.

142

 









dco cptref

Mi Mi

iNi f











(6)

2.1.2. Oscillator

A linear model of the DCO is as follow:









dcoo dco

ifK Cmdi (7)

where fo is the carrier frequency, Kdco the DCO gain and

Cmd the digital command word.

DCO nonlinearity can also be modeled by replacing in

(7) Kdco by a command word dependent-function Kdco

(Cmd).

2.2. Noise Integration

The DCO and the reference signal noises profiles are

based on circuit level simulation or measurement results.

These are converted in time domain by an IFFT before

adding these noises in our models as shown on Figure 5.

By slightly modifying (7), the next equation shows an

easy way to inject DCO noise into the model:













dcoo dconoise

kifKCmd idcoi (8)

where dconoise[i] corresponds to the instantaneous DCO

frequency deviation in accordance with the DCO phase

noise spectral density.

For the reference noise, equation (2) is modified in the

same way. Adding a dither on the reference may be

needed in order to break limit cycles due to TDC nonlin-

earities and then remove the spurs due to them as shown

on Figure 6.

Without reference dithering (in black), the output

phase noise presents a lot of spurious. Adding a dither,

which corresponds directly to a calculus in our model,

allows finding a match between the phase noise obtained

with the formula proposed by Staszewski [7] for the TDC

resolution effect on phase noise used for Laplace model

(in dash) and the one obtained with our model (in grey).

3. Three-points Modulator

Figure 7 shows the impact on WCDMA constellations of

a TDC gain either ideal, but with PLL noises (Figure

7(a)) or truncated (Figure 7(b)) as equation (5) or after

filtering (Figure 7(c)), when the rest of the PLL is con-

sidered noiseless.

Figure 5. Digital P LL with noises .

Figure 6. Output phase noise due to TDC quantization and

dither.

Figure 7. Impact of the TDC gain estimation on WCDMA

constellation.

With an ideal TDC gain and the PLL imperfections,

the EVMrms is about 2%. But if equation (5) is applied

to obtain the TDC gain during the modulation frame,

EVMrms is degraded up to by 14%. Adding filtering on

the gain allows a good reduction of the EVM degradation

depending of the bandwidth of this filtering, but still too

important compared to the impact of the PLL noises.

This shows that the classical measurement method with

filtering cannot work for wideband modulations.

In synthesis mode, the output frequency is locked to

(N+f)fref, so the TDC gain k defined in (5) tends to a con-

stant value. By replacing Tdco[i] by its value in synthesis

mode, the final TDC gain obtained after filtering is:



syn

ref q

kNffT

 (9)

In polar modulation mode, the instantaneous DCO pe-

riod cannot be considered as constant anymore, at least

for wide bandwidth. Looking back on the expression of

the TDC gain defined previously, the equation (5) be-

comes:

 



mod

syn

ref

ki k

Nff





(10)

J. KIEFFER ET AL.

143

Figure 8. Impact of the different methods on EVM.

where ksyn is still the TDC gain in the synthesis mode

defined in equation (10) and which is now calibrated

before inserting the modulation into the PLL. Then, the

modulation, normalized by the wanted output frequency,

is applied on the TDC gain at each sample. This is the

third inputs of the proposed three-points modulator.

The Figure 8 shows the amelioration of the EVM with

the implementation of this new expression instead of

keeping the TDC gain filtered or constant after calibra-

tion. The PLL is still considered perfect.

Several observations can be made thanks to this figure.

At first, it is useless to increase the TDC gain filtering

bandwidth so that most of the modulation can pass with-

out alterations. On the contrary, the EVM increases with

the bandwidth enlargement.

Then, the proposed solution allows an EVM reduction

of 2% compared to a method where the TDC gain is kept

constant after the same calibration (filtering with 10 kHz-

bandwidth in this case). Moreover, the solution presents

certain robustness regarding a calibration error. In others

words, having an offset on the gain estimation has less

impact on EVM than not adding the modulation.The final

EVM is under 1%, below the EVM with the rest of the

PLL imperfections.

4. Conclusions

A nonlinear Digital PLL model has been developed to

bring out the impact of TDC gain estimation in polar

architectures. This causes indeed a large EVM degrada-

tion for wideband modulations such as WCDMA. The

proposed solution which finally amounts to add the mod-

ulation on the TDC gain transforms the classical

two-points modulator in a three-points modulator and

allows a good reduction of the EVM degradation due to

this contributor. This shows that the phase path is not

straightforward for wideband modulations from the con-

clusions derived from GMSK/EDGE polar modulator.

5. Acknowledgements

The authors thank Samuel Dubouloz for his help on the

modulator and demodulator.

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