Why Photomultipliers Need Amplifiers

Dr. A.G. Wright

Although photomultipliers come with versatile internal amplifiers, certain applications also require external amplification.

Photomultipliers remain the preferred light detectors for many applications, mainly because they combine a detection area up to 1500 cm² with electron multipliers — internal amplifiers of exceptional performance. Besides low noise, near-zero offset and low and constant output capacitance, electron multipliers deliver gain up to 10⁸ and bandwidth up to 500 MHz. Given such performance, why should photomultipliers need additional amplification?

In practice, the photomultiplier is one of many elements in a detection system. System designers optimize overall sensitivity by balancing the allocation of gain between the photomultiplier and electronics. Obviously, this requires operating both elements according to which functions they perform satisfactorily.

Photomultipliers perform some functions better than others. External electronic amplifiers help fill in the function and performance gaps, and they have functions other than amplification, such as impedance-matching, bandwidth-limiting and filtering, and pulse-shaping.

Figure 1. Overall sensitivity of a measuring system is proportional to the product of each element’s gain. As illustrated for a scintillation counter where measurements are displayed on a multichannel analyzer, the combination g₁ g₂ g₃ g₄ will achieve the required sensitivity.

Photomultiplier gain declines unpredictably during continuous operation. A significant cause is the total charge taken from the multiplier. External amplification is advisable in applications requiring continuous anode current of more than 1 μA. Using an amplifier with gain of 100, for example, permits a corresponding decrease in photomultiplier gain and, thus, an anode current of only 10 nA.

Peak signal current performance is also a consideration. Photomultipliers with linearly focused dynodes can deliver peak currents up to about 100 mA, or equivalently, a peak signal of 5 V into 50 Ω. Other dynode types do not offer the same peak current capability and may necessitate additional amplification.

All photomultiplier applications fall into three categories: photon counting, pulsed signal measurement and analog detection. All three present occasions in which external amplification is useful.

Figure 2. The equivalent circuit for a photomultiplier is a current generator, in parallel with resistance, R_o, being much greater than 10⁹ Ω and with stray capacitance, C₀, about 5 pF. In this example, the current generator mimics a scintillator with decay time constant τ. Most applications allow analysis in terms of an equivalent R and C combination. Without loss of generality, we can take R = R₀R/(R₀+R) and C = C₁ + C₀.

Photon counting

In photon counting, single photoelectrons initiate photomultiplier output signals. Counters simply tally all of the signals that exceed a fixed voltage threshold. This requires conversion of the current signal into voltage and amplification of the voltage signal to about 50 mV, a level compatible with commercially available discriminators.

Consider a simple resistor, R, connected to the anode to convert current to voltage. This resistor might see a stray capacitance, C, of at least 10 pF contributed by the photomultiplier, the socket and voltage divider board with time constant τ₁ = RC. If a coaxial cable or oscilloscope probe is added, it could easily add another 20 pF of stray capacitance. We can approximate the single electron signal at the anode by:

i(t) = (—eg/τ)exp(—t/τ)
Where e is the electronic charge, g is the gain of the multiplier and τ is the decay time of the photomultiplier pulse. For analysis purposes, an exponential decay is a sufficiently accurate representation of the anode output. The output voltage v₀(t) for such a stimulus is given by:

v₀(t) = —egR/(τ₁ —τ).{exp(—t/τ) — exp(—t/τ₁₎} provided τ ≠ τ₁
This equation suggests that increasing resistance can increase the amplitude, but that also increases τ₁, and if τ₁ is much greater than τ, the equation shows, v₀(peak) amplitude varies inversely with stray capacitance, which should be kept small.

If, as is often the case, an application requires coverage of a wide dynamic counting range, then it requires τ₁ to be comparable to τ. Otherwise, the imposed time constant will broaden the output pulse, leading to overlap and dead-time effects.

Figure 3. In the second equation, stray capacitance, C, is 10 pF; the decay time of the photomultiplier pulse, τ, is 5 ns; and the gain of the multiplier, g, equals 10⁶ for various values of resistance, R. An oscilloscope can confirm the amplitude and the shape of the pulses.

A plot of the second equation (Figure 3) illustrates these points and indicates maximum amplitude of only 1.2 mV when resistance equals 50 Ω. If we are looking for a 50-mV signal, the necessary photomultiplier gain is about 4 x 10⁷. Photomultipliers are capable of operating at this gain, but at a rate of 10 MHz, the mean anode current will be:

I_a = 1.6 x 10^—19 x 4 x 107 x 10⁷ = 64 μA
The photomultiplier will lose gain over time, so it is preferable to seek additional gain from an electronic amplifier. A transimpedance amplifier is ideal for this purpose. It converts input current into output voltage, which is just what’s required.

The second equation also describes output from the amplifier with feedback resistor. This amplifier configuration isolates the voltage-generating resistor from stray capacitance associated with the photomultiplier. A well-laid-out circuit board will limit stray capacitance seen by the resistor to about 0.1 pF and, provided the operational amplifier is sufficiently fast and stable, will allow resistor values up to about 10 kΩ. Such values will provide a peak signal of about 320 mV when photomultiplier gain is 10⁶. It is best to mount the amplifier as close to the anode as possible to minimize input stray capacitance — always undesirable in fast electronics.

Figure 4. Diagram (a) shows current-to-voltage conversion at the anode of a photomultiplier. Diagram (b) illustrates a transimpedance amplifier, which, with its virtual earth input, is ideally suited to current generators such as photomultipliers. The best amplifiers are still made with discrete components, although fast and stable operational amplifiers are now more readily available. In theory, resistance in (b) may be as high as 10 kΩ.

Transimpedance amplifiers offer the additional advantage of low output impedance, typically less than 50 Ω, making them suitable for driving subsequent circuitry without loading the resistor. This isolation is impossible if the resistor is connected directly to the anode, in which case there is no drive capability. An alternative is to use a voltage amplifier, available in a nuclear instrument module unit or, ideally, as a board connected directly to the photomultiplier base. These typically have 50-Ω input impedance and provide gain from 10 to about 100.

Pulsed applications

Most multiphotoelectron applications are in the field of scintillation spectroscopy. However, users may adapt the considerations discussed here to other pulsed applications.

Energetic charged particles can be detected by measuring the light emitted when they interact with an organic scintillator. The decay time constant of the light is typically 1 to 2 ns, comparable with the time resolution of the fastest photomultipliers. The second equation covered this application, but here the pulses are n times bigger — n being the number of photoelectrons in each pulse.

High-density inorganic scintillators are used to detect γ rays. NaI(Tl) is the most widely used material, and it produces about 30 photons per keV of γ-ray energy deposited. A γ-ray of 1 MeV will thus generate about 6000 photoelectrons from a bialkali cathode with an exponential decay time of 240 ns.

Scintillation spectroscopy derives information based on measurement of the rate of events or the size and time of the occurrence of each pulse. Measuring rate is relatively straightforward, but determining the number of photoelectrons in each pulse is more complicated. The ability to see individual photoelectrons in an event decreases with increasing energy. For energies above a few kiloelectronvolts, for instance, individual photodetections may not be separated enough to be counted, leading to underestimation of the event’s energy.

A better way to measure the energy is to integrate the signals and convert the sum of photodetections into a single pulse, the area of which is directly related to the number of photodetections in the event. Connecting the photomultiplier output to a capacitor, C, will integrate each charge pulse, regardless of whether it overlaps. Also, the capacitor will charge to a voltage proportional to the total number of photoelectrons generated.

Again, transimpedance amplifiers are ideal for this purpose. However, in this case, capacitors in the feedback loop perform the integration. The capacitor must discharge between events and, with NaI(Tl) scintillators, it is usual to choose parallel resistors, R, so that τ₁ = CR is about 1 μs, or four time constants. This ensures that the energy determination of the event encompasses most of the output light and enables count rates up to about 20 kHz.

Measuring the occurrence time of each pulse is beneficial if based on the arrival of the event’s first photoelectron, but such low-level detection is not always practical. It is customary to follow the integrating amplifier by a differentiating one. This terminology may be confusing because integration followed by differentiation constitutes a null operation, so why do it? The processes involved, in fact, bear only similarities to differentiation and integration, but the terminology is well-entrenched.

An amplifier with a capacitor at its input passes no direct current, so the unipolar pulses (Figure 5a) are converted to bipolar pulses. The time of zero crossing is independent of pulse amplitude, which is highly desirable in critical timing applications.

Figure 5. In diagram (a), capacitor C integrates output from the photomultiplier producing an output v(max) of about Q/C. Readers can verify that a 1 MeV γ producing 6000 photoelectrons will generate a 1-V output for C = 100 pF with photomultiplier gain = 10⁵. Diagram (b) indicates that the “differentiating” amplifier produces bipolar pulses that cross the time axis at a common point. A zero-crossing discriminator detects the time of occurrence of this point.

Analog applications

Film scanning, an analog application, attaches a positive film to a rapidly rotating drum and exposes it to a sharply focused intense light source. The light source and a photomultiplier, which detects light reflected from the film, traverse the drum to scan its contents for subsequent digitization by an analog-to-digital converter. Bandwidth is the key parameter here and must be optimized according to the speed of the drum and the required pixel size. High-resolution machines may require bandwidths up to 5 MHz.

Once again, the best way to provide the required bandwidth is to use a transimpedance amplifier.

An intense light source ensures high resolution and minimum scan time. A photomultiplier with only six dynodes provides comparatively low gain, in the 10³ to 10⁴ range. It is important in these applications to maintain a mean anode current below 1 μA to ensure stable gain. Excursions up to 100 μA are permissible, but only for short periods of time.

Important points to remember include:

• The photomultiplier is a current generator that produces a charge pulse. For encoding, it requires conversion to a voltage.

• The output may contain unwanted fine structure, and amplifiers achieve pulse smoothing and shaping.

• Amplifiers can eliminate photomultiplier fatigue by providing a portion of overall system gain.

Meet the author

A.G. Wright is the marketing director at Electron Tubes Ltd. in Ruislip, UK. He holds a PhD in physics.