Phase Lock Loop (PLL) - Revision history

Paulo.Pombal: /* Performance */

2016-11-04T15:41:43Z

Performance

← Older revision		Revision as of 15:41, 4 November 2016
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	*<math>\lambda\,</math> is wavelength of the carrier signal [m].		*<math>\lambda\,</math> is wavelength of the carrier signal [m].
	*<math>B_n\,</math> is the loop bandwidth [Hz].		*<math>B_n\,</math> is the loop bandwidth [Hz].
	*<math>C/N_0\,</math> is the carrier to noise ratio [~~dB-~~Hz].		*<math>C/N_0\,</math> is the carrier to noise ratio [Hz].
	*<math>T\,</math> is the integration time [s].		*<math>T\,</math> is the integration time [s].

Filipe.Pelica: Included editor logo.

2014-09-18T16:36:44Z

Included editor logo.

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	\|Level=Advanced		\|Level=Advanced
	\|YearOfPublication=2011		\|YearOfPublication=2011
			\|Logo=GMV
	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
	}}		}}

Carlos.Lopez at 11:01, 23 February 2012

2012-02-23T11:01:43Z

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	{{Article Infobox2		{{Article Infobox2
	\|Category=Receivers		\|Category=Receivers
	\|Editors=GMV ~~A.D.~~		\|Editors=GMV
	\|Level=Advanced		\|Level=Advanced
	\|YearOfPublication=2011		\|YearOfPublication=2011

Carlos.Lopez at 10:35, 23 February 2012

2012-02-23T10:35:09Z

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	{{Article Infobox2		{{Article Infobox2
	\|Category=Receivers		\|Category=Receivers
	\|~~Title={{PAGENAME}}~~		\|Editors=GMV A.D.
	~~\|Authors~~=GMV
	\|Level=Advanced		\|Level=Advanced
	\|YearOfPublication=2011		\|YearOfPublication=2011
	\|~~Logo~~=~~GMV~~		\|Title={{PAGENAME}}
	}}		}}
	Phase Lock Loops are part of the receiver's signal tracking loops, and aim at tracking the phase of the incoming GNSS signal. The PLL provides a correction of the phase in a continuous loop, generating a phase error signal.		Phase Lock Loops are part of the receiver's signal tracking loops, and aim at tracking the phase of the incoming GNSS signal. The PLL provides a correction of the phase in a continuous loop, generating a phase error signal.

Rui.Pereira: moved Work in Progress:Phase Lock Loop (PLL) to Phase Lock Loop (PLL) over redirect

2011-05-27T15:53:30Z

moved Work in Progress:Phase Lock Loop (PLL) to Phase Lock Loop (PLL) over redirect

← Older revision	Revision as of 15:53, 27 May 2011
(No difference)

Rui.Pereira: moved Phase Lock Loop (PLL) to Work in Progress:Phase Lock Loop (PLL)

2011-05-11T13:37:11Z

moved Phase Lock Loop (PLL) to Work in Progress:Phase Lock Loop (PLL)

← Older revision	Revision as of 13:37, 11 May 2011
(No difference)

Rui.Sarnadas at 13:40, 6 May 2011

2011-05-06T13:40:06Z

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	~~ans~~ another example of Costas loops is given by:		and another example of Costas loops is given by:

Rui.Sarnadas at 13:39, 6 May 2011

2011-05-06T13:39:21Z

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			Phase Lock Loops are part of the receiver's signal tracking loops, and aim at tracking the phase of the incoming GNSS signal. The PLL provides a correction of the phase in a continuous loop, generating a phase error signal.
	Phase Lock Loops are part of the ~~Tracking Loops~~ and aim at tracking the phase of the incoming GNSS signal~~, providing~~ a correction of the phase in a continuous loop.


	==Principle ==		==Principle ==
			The '''Phase Lock Loop (PLL)''' tracks and estimates the current misalignment between the [[Correlators\|Prompt correlator]] and the incoming signal phase, within the [[Tracking Loops\|tracking loops]]. For that purpose, the PLL uses integrations, filters and Numerical Control Oscillators (NCO) – described [[Tracking Loops\|here]] – as any other typical loop. In this case, the specificity relies on the discriminator used to assess the current phase error estimated at the receiver.
	The Phase Lock Loop (PLL) tracks and estimates the current misalignment between the [[Correlators\|~~prompt~~ correlator]] and the incoming signal phase, within the [[Tracking Loops\|tracking loops]].
	For that purpose, the PLL uses integrations, filters and Numerical Control Oscillators (NCO) – described [[Tracking Loops\|here]] – as any other loop.
	~~The~~ specificity relies on the discriminator used to assess the current phase error estimated at the receiver.

	~~As elaborated [[Baseband Processing\|previously]], the output of the correlation and accumulation blocks can be written in its in-phase (I) and quadrature (Q) components as:~~

	[[File:pll_principle.png\|right\|thumb\|350px\|'''''Figure 1:''''' Representation of the Prompt Correlator output.]]		[[File:pll_principle.png\|right\|thumb\|350px\|'''''Figure 1:''''' Representation of the Prompt Correlator output.]]
			As elaborated [[Baseband Processing\|here]], the output of the correlation and accumulation blocks can be written in its ''In-phase (I)'' and ''Quadrature (Q)'' components as:


	<math>I_P = A_X d_X R_X (\tau_e) cos(\phi_e) </math>		<math>I_P = A_X d_X R_X (\tau_e) cos(\phi_e)\,</math>

	<math>Q_P = -A_X d_X R_X (\tau_e)sin(\phi_e) </math>		<math>Q_P = -A_X d_X R_X (\tau_e)sin(\phi_e)\,</math>


	where		where:
	*<math>R_X</math> is the auto-correlation of the X PRN code		*<math>R_X\,</math> is the auto-correlation of the ''X'' PRN code.
	*<math>P</math> stands for the Prompt replica, i.e. the replica generated at the receiver which is aligned with the incoming signal		*<math>P\,</math> stands for the ''Prompt'' replica, i.e. the replica generated at the receiver which is aligned with the incoming signal.
	*<math>\tau_e</math> is the error of the code delay estimated at the receiver		*<math>\tau_e\,</math> is the error of the code delay estimated at the receiver.
	*<math>\phi_e</math> is the error of the carrier phase estimated at the receiver		*<math>\phi_e\,</math> is the error of the carrier phase estimated at the receiver.


	Figure 1 represents the output of the In-phase and Quadrature components of the prompt correlator. When tracking the signal correctly, the prompt vector should be, ideally, in the In-phase axis (with no Quadrature component). Therefore the phase error can be retrieved from the phase of the correlator using <math>P_I</math> and <math>P_Q</math> and the PLL will feedback a new carrier correction in order to minimize this error.		Figure 1 represents the output of the In-phase and Quadrature components of the prompt correlator. When tracking the signal correctly, the prompt vector should be, ideally, in the In-phase axis (with no Quadrature component). Therefore, the phase error can be retrieved from the phase of the correlator using <math>P_I\,</math> and <math>P_Q\,</math>, and the PLL will feedback a new carrier correction in order to minimize this error.

	==Discriminators ==		==Discriminators ==
			Two types of PLL discriminators are often mentioned<ref name="kaplan">Kaplan E.D., Hegarty C.J., "Understanding GPS: Principles and Applications", second edition.</ref>:

	~~Two types of Phase Lock Loop discriminators are often mentioned <ref name="kaplan">Kaplan E.D., Hegarty C.J.,"Understanding GPS: Principles and Applications", second edition</ref>:~~

			*'''Sensitive to bit transitions, hence phase shifts''':

	*Sensitive to bit transitions~~, hence phase shifts~~		The most common discriminator sensitive to bit transitions is given by:

	~~The most common discriminator sensitive to bit transitions is given by:~~

	<math>\phi_e =ATAN2(Q_P,I_P)</math>		<math>\phi_e =ATAN2(Q_P,I_P)\,</math>


	which is optimal but presents a high computational burden. In order to use such discriminator, the receiver must ensure that the inputs do not include bit transitions, e.g. doing data wipe-off during the integration.		which is optimal, but presents a high computational burden. In order to use such discriminator, the receiver must ensure that the inputs do not include bit transitions, e.g. doing data wipe-off during the integration.


	*Insensitive to bit transitions; also called Costas loop		*'''Insensitive to bit transitions, also called Costas loop''':

	The classic Costas loop discriminator (the near optimal) can be written as:		The classic Costas loop discriminator (the near optimal) can be written as:

	~~<math>sin(2\phi_e) =Q_P \times I_P</math>~~

			<math>sin(2\phi_e) =Q_P \times I_P\,</math>

	~~Other examples of Costas loop include:~~

	~~<math>tan(\phi_e) =Q_P / I_P</math>~~		ans another example of Costas loops is given by:

	~~<math>\phi_e =ATAN(Q_P / I_P)</math>~~

	The choice of the discriminator is a trade-off between performance of the PLL and required hardware resources as well as complexity.		<math>tan(\phi_e) =Q_P / I_P\,</math>


			The choice of the discriminator is a trade-off between performance of the PLL and required hardware resources, as well as complexity.

	==Performance ==		==Performance ==
			The main sources of errors in the PLL are phase jitter and dynamic stress error<ref name="kaplan"></ref>, which are mainly produced by thermal noise. The PLL thermal noise jitter for an arctangent PLL can be written (in meters) as:

	~~The main sources of errors in the PLL are phase jitter and dynamic stress error <ref name="kaplan"></ref>, which are greatly produced by thermal noise.~~
	~~The PLL thermal noise jitter for an arctangent PLL can be written (in meters) as:~~

	<math>\sigma_{th}=\frac{\lambda}{2 \pi} \sqrt{\frac{B_n}{C/N_0}(1+\frac{1}{2TC/N_0})}</math>		<math>\sigma_{th}=\frac{\lambda}{2 \pi} \sqrt{\frac{B_n}{C/N_0}(1+\frac{1}{2TC/N_0})}\,</math>

	~~Where~~
	*<math>\lambda</math> is wavelength of the carrier signal [m]
	*<math>B_n</math> is the loop bandwidth [Hz]
	*<math>C/N_0</math> is the carrier to noise ratio [dB-Hz]
	*T is the integration time [s]

			where:
			*<math>\lambda\,</math> is wavelength of the carrier signal [m].
			*<math>B_n\,</math> is the loop bandwidth [Hz].
			*<math>C/N_0\,</math> is the carrier to noise ratio [dB-Hz].
			*<math>T\,</math> is the integration time [s].

	~~The performance of the PLL depends mainly on the loop bandwidth and the integration times used to accumulate the correlator outputs.~~
	~~The impact of these parameters is shown in Figure 2, and they are visible mainly for low carrier to noise ratio.~~

			The performance of the PLL depends mainly on the loop bandwidth and the integration times used to accumulate the correlator outputs. The impact of these parameters is shown in Figure 2, and they are visible mainly for low carrier to noise ratio.

	[[File:pll_performance.png\|center\|thumb\|550px\|'''''Figure 2:''''' Impact of loop bandwidth (left) and integration time (right) on the PLL thermal noise jitter performance.]]		[[File:pll_performance.png\|center\|thumb\|550px\|'''''Figure 2:''''' Impact of loop bandwidth (left) and integration time (right) on the PLL thermal noise jitter performance.]]

			These results also illustrate the fact that longer integration times (and lower bandwidths) lead to noise reduction, hence higher performances, as discussed [[Tracking Loops\|here]].
	These results also illustrate the fact that longer integration times (and lower bandwidths) lead to noise reduction ~~and~~ hence higher performances, as discussed [[Tracking Loops\|~~previously~~]].

	==Related articles==		==Related articles==
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	==References==		==References==
	<references/>		<references/>


	[[Category:Receivers]]		[[Category:Receivers]]

Teresa.Ferreira: /* Discriminators */

2011-05-05T22:44:49Z

Discriminators

Teresa.Ferreira: /* Principle */

2011-05-05T22:42:35Z

Principle

← Older revision		Revision as of 22:42, 5 May 2011
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	where		where
	*<math>R_X</math> is the auto-correlation of the X code		*<math>R_X</math> is the auto-correlation of the X PRN code
	*<math>P</math> stands for the Prompt replica, i.e. the replica generated at the receiver which is aligned with the incoming signal		*<math>P</math> stands for the Prompt replica, i.e. the replica generated at the receiver which is aligned with the incoming signal
	*<math>\tau_e</math> is the error of the code delay estimated at the receiver		*<math>\tau_e</math> is the error of the code delay estimated at the receiver
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	Figure 1 represents the output of the In-phase and Quadrature components of the prompt correlator. When tracking the signal correctly, the prompt vector should be, ideally, in the In-phase axis (with no Quadrature component). Therefore the phase error can be retrieved from the phase of the correlator using <math>P_I</math> and <math>P_Q</math> and the PLL will ~~act so as~~ to minimize this error.		Figure 1 represents the output of the In-phase and Quadrature components of the prompt correlator. When tracking the signal correctly, the prompt vector should be, ideally, in the In-phase axis (with no Quadrature component). Therefore the phase error can be retrieved from the phase of the correlator using <math>P_I</math> and <math>P_Q</math> and the PLL will feedback a new carrier correction in order to minimize this error.

	==Discriminators ==		==Discriminators ==

← Older revision		Revision as of 22:44, 5 May 2011
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	*Sensitive to bit transitions, hence phase shifts		*Sensitive to bit transitions, hence phase shifts

	The most common discriminator sensitive to bit transitions is		The most common discriminator sensitive to bit transitions is given by:

	<math>\phi_e =ATAN2(Q_P,I_P)</math>		<math>\phi_e =ATAN2(Q_P,I_P)</math>
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	*Insensitive to bit transitions; also called Costas loop		*Insensitive to bit transitions; also called Costas loop

	The classic Costas loop discriminator ~~is given by~~ the near optimal:		The classic Costas loop discriminator (the near optimal) can be written as:

	<math>sin(2\phi_e) =Q_P \times I_P</math>		<math>sin(2\phi_e) =Q_P \times I_P</math>


	Other examples of Costas loop include		Other examples of Costas loop include:

	<math>tan(\phi_e) =Q_P / I_P</math>		<math>tan(\phi_e) =Q_P / I_P</math>
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	<math>\phi_e =ATAN(Q_P / I_P)</math>		<math>\phi_e =ATAN(Q_P / I_P)</math>

	The choice of the discriminator is a trade-off between performance of the PLL as well as ~~the required hardware resources and~~ complexity.		The choice of the discriminator is a trade-off between performance of the PLL and required hardware resources as well as complexity.

	==Performance ==		==Performance ==