PHASE NOISE SOURCES AND EFFECTS

As already discussed in Chapter 3 the ultimate synchroscan resolution is limited by phase noise in the drive signal. Since the tunnel diode system showed improved performance compared to the passive system the effect of phase noise in the drive signal was examined in more detail, the deviating effect of noise being extended to accommodate a general noise floor distribution rather than the specific sidebands considered in the previous chapter.

There are several possible sources of phase noise in the synchronisation circuitry; part is laser-related and part is generated internally in the electronics. Laser pulse train amplitude fluctuations are monitored as a modulation in the initial photodiode electrical signal. The effect of ampliude modulation inside the limiter has already been discussed, but there is an

analogous effect in the tunnel diode system. Any variation in switching current implies a triggering jitter between points A and B' and hence once more laser amplitude fluctuations are mapped into phase modulations in the synchroscan drive signal. Thus, although the laser source is inherently stable in terms of phase noise, severe constraints are placed upon the constancy of its pulse train amplitude for both synchronisation techniques.

The active system has the advantage over its passive counterpart in that relatively high signal levels are maintained throughout and thus the system has a improved signal-to-noise ratio at the input. This will only be important if the main noise source is not from laser amplitude fluctuations but from the photodiode itself. In addition the active circuit will also be less susceptible to electromagnetic interference which can be a problem with the high gain and high deflection powers employed. Fundamental noise sources, eg. Johnson noise in the input stage, may also be less influential in the active system which has a lower source resistance, although it is difficult to quantify this figure for the two systems.

Carrier Tuning characteristic of system T(f) Noise floor Vn(‘)

t

Figure 4.6 Representation of phase noise and drive signal in synchroscan circuitry.

To determine the effect of such broadband noise sources on the achievable temporal resolution during synchroscan operation a more detailed theoretical analysis was

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'" i

I

p e rfo rm e d In this analysis the input drive signal is treated as a single component of frequency f© which sits on a noise floor having an instantaneous amplitude Vn(t) and random fluctuation (See Fig. 4.6). The noise floor is assumed to originate from many sources but can be taken to have a uniform spectral distribution which will be tailored by the tuning characteristics of the circuit, T(f). (This is not necessarily true for a nonlinear limiting circuit but for the purposes of this preliminary analysis this was ignored.) The instantaneous integrated deviating voltage is given by :

DO

VN(t) = JVn(t).T(f).exp{i[0(f,t)])df -eq(4.1)

o

where Vn(t) is the instantaneous amplitude of a noise sideband frequency component at frequency f and 0(f,t) is its instantaneous phase. T(f) is the tuning characteristic of the electronic circuit which will act to tailor the noise floor frequency distribution. Effectively VN(t) is the sum of a continuous set of uncorrelated oscillators weighted by the bandpass response of the system. Evaluation of the distribution of deviating voltages represented in equation 4.1 is extremely difficult using numerical techniques without knowledge of the noise floor distribution. Nonetheless, since noise content in a signal is often measured in terms of noise power within a given bandwidth it is instructive to represent Vn by a

Gaussian distribution:

where Vm is the root mean square voltage obtained from the noise power appearing at the deflector plates and its variance, AVm^ taken as a fixed percentage of the mean. Hence the instantaneous drive signal applied to the deflector is given by the sum of the carrier and the deviating noise contribution such that:

Vs(t) = Im.[Vcexp{i(27tfot)) + VN(t)exp{i0}] -eq(4.3) where 0 , the phase of the deviating integrated noise voltage, will be uniformly distributed between 0 and 27t. For a particular streak operation the deviating voltage is calculated by a Monte-Carlo method.

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The electron trajectory within the streak tube was calculated by the Runge-Kutta technique (§2.5) where the potential distribution of the Photochron IV was determined by a finite difference solution of the Laplace equation. The computational process and the various distribution functions used are summarised schematically in Fig.4.7.

Input pulse profile I(t) = I(^xp{-(t/At)^} Runge-Kutta trajectory calculation Electron-lens _Deflectors Photocathode Electron distribution in energy and emergent angle N(e,0,0 ) = B (mji) F(0.0)

Deflection term _Phosphor

Electron spatial density distribution

N(x)

Figure 4.7 Schematic of calculation process used in computer model.

A Gaussian input optical pulse profile of duration 300 fs was assumed. The distribution of electron energies leaving the photocathode was modelled by a Beta function and the distribution in exit angles modelled by a Lambertian function giving uniform and cosine distribution for angles in the photocathode plane and normal respectively Again a Monte-Carlo technique was used to generate the initial values. For each streak the electron density distribution appearing at the deflectors was computed and the above expression representing the total deflection voltage was then mapped onto this distribution to generate a spatially varying electron density profile at the phosphor screen. The magnitude and phase of the deviating noise voltage was assumed not to vary as the electron distribution was deflected on the basis that the bandwidth of the deflection system would limit fluctuations to a few megahertz and consequently during the transit time of the electrons through the plates (-0.5 ns) any additional variation of the deviated deflection voltage would be minimal. Provision was made for a second term in the input pulse profile to represent jitter between the laser and the deflection signals. These calculations were then performed over a

total of 104 streaks and an integrated spatial electron density profile N(x) was generated. With a knowledge of the streak velocity (0.65 x 10^ cms'l @ 15 Watts) N(x) was transformed into a temporal spread distribution from which the temporal resolution was deduced. This process was repeated for a range of noise powers.

A I &

!

Mean integrated noise relative to carrier (dBc)

Figure 4.8 Achievable temporal resolution as a function of integrated noise level with respect to carrier signal.

Figure 4.8 shows the expected temporal resolution as a function of integrated noise level with respect to the carrier signal (201ogio(Vc/Vn)). Note that for noise levels below 80 dB with respect to the drive signal the achievable resolution is almost equal to the theoretical tube limiting temporal resolution. Between 80dB and 70dB temporal response begins to be degraded until at 60dB the available resolution is nearly 2 ps which exceeds the limiting temporal resolution by a factor of more than three.

4.5 NOISE LEVELS IN PASSIVE AND ACTIVE SYNCHRONISATION SYSTEMS