chapter 5

Circuit Response

• A 1 μF capacitor placed across a 1kΩ resistor has a time constant of 1 ms.
• After a long time (t » 5RC), the voltage approaches its final (equilibrium) value.
• The 5RC rule states that a capacitor charges or decays to within 1% of its final value after about five time constants.

CR Differentiator or High-Pass Filter

• The output of a single CR differentiating circuit has several unwelcome features for pulse processing systems.
• The sharp top makes any subsequent pulse height analysis difficult.
• All high-frequency noise components are passed through by the circuit, implying that the signal-to-noise ratio is usually poor.

CR – RC Shaping

• The combination of a CR differentiator and RC integrator is commonly used as a pulse shaper in linear amplifiers.
• If an RC integrating stage follows the CR stage, both of the unwelcome features mentioned above can be much improved.
• The use of an operational amplifier (op amp) provides impedance isolation, isolating the two individual networks.

Pulse Shape Analysis (PSA)

• PSA involves analyzing the shape of the pulse to get information on the interaction position (particle tracking).
• Radiation interaction can happen anywhere in the detector sensitive material.
• Pulses from interactions near the collecting electrode have shorter rise times.

Pulse Shaping

• The shapes of signal pulses from detectors are usually changed or shaped by the signal conditioning or processing elements of the data acquisition system (DAC).
• Preamplifier signal has a short rise time and long decay time.
• Shaping of the pulse is necessary to get information from the pulse with high precision: pulse height, pulse width, rise time, and fall time.

Pulse Characteristics

• A pulse has height (amplitude), width, rise time, and decay time.
• Baseline is the voltage (current) level to which the pulse decays (usually set to zero).
• Pulse height (amplitude) is the height of the pulse measured from the baseline to its maximum.
• Signal width is usually taken as the FWHM.
• Leading edge is the flank of the signal that comes first in time.
• Trailing edge is the flank of the signal that comes last in time.
• Rise time is the time it takes the pulse to rise from 10% to 90% of the full amplitude.
• Fall time is as for rise time, but related to the decay of the pulse.

Pulse Defects

• Typical pulse defects are overshoot, ringing, tilt, and undershoot.
• Overshoot is due to electronic CR-RC networks.
• Ringing is due to reflections in the transmission lines.
• Tilt is due to attenuation.
• Undershoot is due to electronic CR-RC networks.

Pulse Types

• Signal pulses can be unipolar or bipolar.
• Slow pulses have slow rise time compared to transit time (‘t’rise > 100ns) and are generated by linear devices.
• Fast pulses have fast rise time compared to transit time (‘t’rise ~ 1ns) and are used for timing and high count rate applications.