OSCILLATOR GENERATED PHASE NOISE ON DS-CDMA
6.3 Amplitude (AM) uois e
AM noise which is generated by the LO source is injected into the mixer along with the LO signal. This noise is severe when the LO signal is generated at a low level and amplified.
A mixer's LO signal can be generated in many ways. The simplest is to use some type of oscillator operating directly at the LO frequency. In some cases, the LO signal is generated initially at a subharmoruc of the desired LO frequency and multiplied to the desired frequency. The frequency multiplier often requires a high input level, and it is necessary to amplify the original subhamlonic signal substantially. Amplifying the LO adds a certain amount of noise. This noise is AM noise; it consists of variations in the amplitude of the LO signal and can be treated as an additive noise process. When the noisy LO signal is applied to the mixer, its AM noise components at the RF and image frequencies are downconverted and appear at the IF port just as if they had been applied to the RF input. Therefore, the mixer noise temperature (or noise figure) is increased by an amount, depending on the type of mixer used, may be as high as the
6·2
IMPACf OF LO GENERATED PHASE NOISE ON DS·CDMA PERFORMANCE CHAPTER 6
La
noise temperature. Ifno measures are taken to eliminate theLa
noise, the increase in the mixer's noise temperature may be very great.The AM
La
noise can be reduced by straight-forward techniques to a level where it is insignificant. The IF frequency is picked up high enough so that the RP and image frequencies are well separated from theLa
frequency, so the noise at these frequencies can be removed effectively by filtering. The fF frequency should typically be at least 5% to 10% of theLa
frequency if it is expected that AM noise will have to be removed by filtering. This may require a trade-off with IF amplifier noise temperature, since amplifier noise temperatures generally rise with frequency.The general fonn of the expression for the output wave from a noisy oscillator can be written as
V(t)~
[voH(t)~os [ 2iifot+I'(t)1
wherelo = nominal oscillation frequency Vo = nominal oscillation amplitude E(I) = fluctuations in amplitude rKI) = fluctuations in phase
(6.1 )
Equation (6.1) indicates there is a concentration of noise power surrounding the RF local oscillator signal. A typical spectral distribution of such a signal is shown in figure (6.1).
{, Frequency
•
Fig. 6.1: Noise spectrum of a RF local oscillator signal (from 171])
In general, both the AM noise and FM or phase noise, &(1) and r/(I), respectively are present, accounting for the lack of symmetry in the envelope of the spectrum. The AM
IMPACT Of LO GENERATED PHASE NOISE ON OS-COMA PERfORMANCE CHAPTER 6
noise component in this instance is negligible when compared to the phase/frequency noise component [72]. Thus it is often neglected in the analysis of phase noise.
6.3.1 Analysis
6.3.1.1 Sinusoidal modulation
With the phase noise component~(I)=O, equation (6.1) can be rewritten as V(f} ;
[vo
+£(f})::os(21ifof)Letting E(r) = Eo cos(ro .. mt} , equation (6.2) can be written as
V(r) =
lv
o + E 0 cos(ro ANI} Jcos{O) of)= v 0 cos(ro 01) + & 0 cos(ro ANt )cos(ro ot)
=Vo COS(WofJ+
E; ~OS ((J)o
+(r)AN)I+COS((J)o-roAN)']
(6.2)
(6.3)
where roAN ::2njAN is angular frequency of modulation and roD =2rr./o is the angular oscillation frequency.
The spectrum of a sinusoidally amplitude-modulated sinusoidal signal consists of three unmodulated sinusoidal signals located at three frequencies:Io,Io-/AN,Io+ fAN (figure (6.2))
v
•'
£
,
2 £ 2"
4 4
f,
Fig. 6.2: Spectrum of sinusoidallv amplitude-modulated sinusoidal signal
The vectorial representation of this consists of a vector of amplitude Vo rotating at (00 and two vectors of amplitude &012 rotating at (00 + roAN and roo - roAN, whose resultant is collinear with V, (figure (6.3)).
6-4
IMPACT OF LO GENERATED PHASE NOISE ON OS-COMA PERFORMANCE CHAPTER 6
AM vector I
v
o
2n1,;Fig. 6.3: Vector representation of sinusoidally amplitude-modulated sinusoidal signal
The maximum signal power is:
p.~
=~, [v. +{ E; )]'
(6.4)The minimum signal power is:
Pm"
= ::' [v. _{ E; )]'
(6.5)The fluctuation in power is then
(6.6)
6.3.1.2 Modulation bv noise
By assuming that the modulating signal is noise of spectral density S(fANJ, the spectrum can be broken down into elementary components separated by differences in frequency of/m and each located within a frequency band Llf(ligure (6.4)).
Com!r
Upper i,C!coond
Fig. 6.4: Representation of a wave modulated by noise (from 169))
IMPACT OF LO GENERATED PHASE NOISE ON OS-COMA PERFORMANCE CHAPTER 6
The nOIse power can then be represented in each frequency band by a sinusoidal generator with a frequency equal to that of the centre of the band concerned and with an amplitude proportional to ~2S(/tN )6/ (the proportionality coefficient takes account of the modulation of the oscillator by the noise). The general spectrum will have the form shown in figures (6.2) and (6.3), but there will he many vectors rotating with angular velocities distributed uniformly in a continuum. The above relationships are then valid for each equivalent generator and thus for the entire noise modulation.
Measurement of AM noise is generally achieved by applying the complete spectrum to a square-law detector of sensitivity S which produces fluctuations in steady voltage corresponding to the fluctuations of power produced by the noise. The voltage fluctuations then undergo standard low-frequency treatment for noise measurement. If S = LlVI.:1P and if an index for AM noise is defined by:
M . . d .:N"o"is",e,:-"p-=o-,-\\-='ec,r:..:i"Il:..:'"h"e-=S.::id"e:.:b"o",ll-=d=-s
A IIOlse 1II ex = -
Power ill the carrier (6.7)
[
(AV'ff I SP,,)' ]
or AM noise index = 10 log,o 4 (6.8)
in dB with respect to the carner (dBc). The index is given in dBcHz-1•