6.5. Photodetectors 391
Imax0.9Imax0.1ImaxPhoton PulseAnode PulseTransit TimeRise Time Decay Time TimePulseHei
ghtFigure 6.5.19: Time response of a PMT to a very narrow incident
photon pulse.Imaxis the highest measured anode current (or pulse
height).voltage distribution. There are also other types of PMTs, most notably the ones
with multi channel plate structures, come close and sometimes surpass the timing
performance of the linear focused type PMTs.
A.13FrequencyResponse
The frequency response of PMTs is of significance for tubes working at high rates,
specially the ones that are used for timing applications. In most applications one is
interested in determining thecutoff frequency, that is, the frequency beyond which
the tube’s response falls below some acceptable value. In the previous section we
studied the time response of PMTs. Although sometime the time response and
frequency response are used interchangeably in literature but we will keep them
separate even though they are closely related. The rationale behind this separa-
tion is simply the importance of the cutoff frequency that does not appear in the
time response characteristics. Another factor that should be noted is that the time
response of a PMT depends largely on its mechanical structure. The frequency re-
sponse, on the other hand, depends not only on the mechanical structure but also
on the external readout circuitry.
The dependence of the frequency response on the external circuitry can be ap-
preciated from the following formula for the cutoff frequency.
fc=1
2 πCsRl,eff(6.5.21)
HereCsis the total capacitance at the output andRl,effis theeffectiveload re-
sistance. The reader might recall that the load resistance is used to convert the
output current into voltage and that the voltage is actually measured across it (cf.
Fig.6.5.14). However it should be noted that the subsequent amplifier has its own
input resistance too, as shown byRain Fig.6.5.20. This implies that the effective