(p.398) Appendix II Fast Signal Measurements
(p.398) Appendix II Fast Signal Measurements
Chemical and physical events occur over a wide dynamic time range. Many atomic and molecular processes occur at “fast” rates in the microsecond (10−6 sec), nanosecond (10−9 sec), or even picosecond (10−12 sec) time domains. The experimental observation of these processes, therefore, requires fast observation methods, usually involving fast time-dependent electronic-signal processors. Time-dependent signal detection is employed throughout this book in every experiment detecting light with photodiodes or PMT detectors, or detecting ions or electrons with electron multiplier tubes or microchannel plates. Digital oscilloscopes, photon counters, and boxcar integrators are all examples of fast electronic-signal processors. It is therefore important to consider the appropriate equipment operation and techniques for these measurements. 
Detectors used in electronics experiments produce an electrical current, I, when a signal is detected. For example, when a photon strikes a photodiode or a photomultiplier tube, a photo-current is produced. However, electronic devices such as oscilloscopes usually display or measure the corresponding voltage, V, resulting from driving this current into a load resistor, R. The current and voltage are related according to Ohm’s Law, V = IR. This relation applies exactly when the units of the quantities are volts, amps, and ohms, respectively. Thus, if a signal current of 3 microamps is detected with an oscilloscope into a 1 megohm resistor (a typical value), the voltage intensity displayed on the oscilloscope will be
Smaller load resistors produce a corresponding smaller voltage for the same input current. To make the signal appear larger on an oscilloscope, therefore, a larger load resistor should be used.
Additional considerations about the signal are required when this current or voltage changes rapidly with time. This is because all electronic equipment, including the processors themselves and even the wires and connectors used to carry the signal, have characteristic time-response limitations. For example, a 100 MHz oscilloscope cannot detect any signals varying with a frequency greater (p.399) than this value. Its response is then limited to events occurring on a timescale τc, such that
Voltage signals changing faster than 10 nsec will therefore not be measured accurately by this instrument.
The time limitation in electronic equipment occurs because of the capacitance, C, in its components. Capacitance occurs whenever conductors and non-conducting materials (insulators) are used together, as in all electronic components. Because of capacitance, the movement of electrical charge (current) is limited to a response time given by,
where R is the load resistance in ohms and C is the capacitance in Farads. This is often referred to as the RC time constant of the circuit. The flow of charge through wires or other components is always limited by this charging time, which affects both the rise and fall of electrical signals. The response is exponential in nature (following first-order kinetics), so that the fall of a current can be expressed as
As usual, for exponential decays, the value τc occurs when the signal intensity (current) has dropped to 1/e of its initial value I(0).
The coaxial cables used in typical laser labs have a capacitance of approximately 10 picoFarads per foot. A typical cable of length 10 ft. therefore has about 100 pFd capacitance. If this is used with a typical load resistor on an oscilloscope of 1 megohm, the time constant for the scope/cable combination is,
Signals faster than 100 μsec will therefore not be measured accurately. If a faster time-dependent signal is to be measured, a larger load (smaller resistor) must be used to decrease the response time. Usually, a 50 ohm load resistor is used. Then,
Notice, however, that reducing the load resistor also reduces the measured voltage (via V = IR). Therefore, there is always a compromise between increasing the speed of a measurement and decreasing the voltage amplitude observed. In other words, conditions that allow fast signals to be measured result in their appearing as small voltages on an oscilloscope.
(p.400) Standard oscilloscopes usually have a setting for 1 megohm input impedance for the detection of signals whose time response is not fast, and a setting for 50 ohm input impedance for detecting fast signals. Unless this setting is chosen correctly, detection of fast signals from photon, ion, or electron detectors cannot be accomplished properly.