General Description
The CR-200 is a single channel shaping amplifier, intended to be used to read out the signals from charge sensitive preamplifiers. Gaussian shaping amplifiers (also known as pulse amplifiers, linear amplifiers, or spectroscopy amplifiers) accept a step-like input pulse and produce an output pulse shaped like a Gaussian function. The purposes of this are to filter much of the noise from the signal of interest and to provide a quickly restored baseline to allow for higher counting rates. The CR-200 is available in 7 different shaping times: 100 ns, 250 ns, 500 ns, 1 μs, 2 μs, 4 μs, and 8 μs. Each has a fixed gain of 10. If additional gain is desired, it is recommended that this be done with the application of an additional amplifier between the preamplifier and the CR-200 shaping amplifier. Cremat offers an evaluation board (CR-160) which includes a multi-stage variable-gain amplifier, as well as all necessary connectors.

Definition of "Shaping Time"
The shaping time is defined as the time-equivalent of the „standard deviation“ of the Gaussian output pulse. A simpler measurement to make in the laboratory is the full width of the pulse at half of it’s maximum value (FWHM). This value is greater than the shaping time by a factor of 2.4. For example, a Gaussian shaping amplifier with a shaping time of 1.0 μs would have a FWHM of 2.4 μs.

Pole/Zero Correction
The long decay time of the input pulse creates a small overshoot in the shape of the ≠output pulse unless a pole/zero correction is utilized. This can be done by connecting a resistor (RP/Z) between pin 1 (input) and pin 2 (P/Z). This resistor is in parallel with the input capacitor (internal to the CR-200 circuit) and creates a ’zero’ in the amplifier’s transfer function which cancels the ’pole’ created by the charge sensitive preamplifier’s feedback resistor. To achieve proper pole/zero cancellation, RP/Z should be selected to be equal to Rf*Cf/Cin where Rf and Cf are the feedback resistor and feedback capacitor of the charge sensitive preamplifier and Cin is the value of the input capacitor in the CR-200. The value of Cin for the CR-200 circuit can be found in the provided table.
Keep in mind that adding RP/Z will likely affect the DC offset of the shaping amplifier output. This is because RP/Z directly couples the DC offset from the charge sensitive preamplifier output into the shaping amplifier input. Some fraction of this DC offset is amplified along with the pulse. It is recommended that instrumentation which includes the CR-200 include a DC offset adjustment to be used to correct for this. You may wish to realize RP/Z as a potentiometer so to adjust the value precisely.

Baseline Restoration (BLR)
The CR-200 does not contain active baseline restoration circuitry. For this reason there will be a negative ’baseline shift’ (change in the output DC offset) at high counting rates. In order to determine whether this will be a problem for your application, use the equation (valid for small baseline shifts):
S/H = R * τ * 2.5 x10-6
where S is the negative baseline shift, H is the pulse height, R is the count rate (counts/sec), and τ is the shaping time of the shaping amplifier (in μs). For example, using a 1 μs shaping amplifier we would predict a 0.025 (2.5%) shift in the baseline at a count rate of 10,000 counts per second. The simplest solution to this possible problem is to implement a bipolar shape to the signals. Bipolar shaping is not susceptible to baseline offset shifts with increasing count rate. This can be easily done by differentiating the Gaussian output pulse using a ’C-R’ filter. Suggested values for Cout and Rout are provided in the table presented on the following page. Keep in mind that making the pulse bipolar in this way will reduce the amplitude to less than half the original pulse height and reduce the width to half its previous value.

Package Specifications
The CR-200 circuit is contacted via an 8-pin SIP connection (0.100“ spacing). Pin 1 is marked with a white dot for identification.

Equivalent circuit diagram
Figure 2 shows an equivalent circuit. Pin numbers corresponding with the CR-200 shaping amplifier are shown. Input components Cin and Rin form a differentiating circuit. The following circuitry consists of two Sallen and Key filters, providing 4 poles of integration and signal gain. The numerous integration stages produce an output pulse that approximates a Gaussian function.

Typical Application
Figure 4 shows the CR-200 in a typical application, coupled to a detector via a CR-110 charge sensitive preamplifier. Depending on the requirements of your application, an ACcoupled amplifier may be added between the preamplifier and shaping amplifier to further increase the signal size.

Choosing the Optimal Shaping Time for your Application
There are a number of considerations in the choice of the optimal shaping time foryour application. Consider:
1. The shaping time must be long enough to collect the charge from the detector. This may be a limiting factor in slow detectors such as gas-based drift chambers orwhen collecting the light from slow-decay scintillators.
2. The shaping time must be short enough to achieve the high counting rates yourequire. Assuming randomly spaced pulses, long-shaped pulses have a higher probability of ’piling up’ than short pulses. Note ’pile-up’ will only be a problemat very high count rates; ’Baseline shift’ will start to be a problem at somewhatlower count rates. See the previous section regarding ’Baseline Restoration’.
3. Choose a shaping time that filters as much of the electronic noise as possible.Electronic noise at the preamplifier output is created by a number of differentaspects of the detection system. Some of these ’noise components’ have different
frequency distributions, allowing us to use the filtering capability of the shapingamplifier to choose a shaping time that minimizes the noise for the particulardetection system under design. The principal sources of electronic noise in adetection system are:
a) the thermal noise of the input JFET in the preamplifier (which is proportional tothe total capacitance to ground at the input node),
b) the thermal noise of the feedback resistor and any ’biasing’ resistor attached to the detector,
c) the ’shot noise’ of the detector leakage current,
d) the electrical contact-related 1/f noise of the detector and preamplifier input JFET, and
e) the ’f noise’ caused by the proximity of lossy dielectric material near the preamplifier input node.
Of the noise components listed, the noise from factor (a) is more heavily filtered with longer shaping times. More precisely, the electronic noise due to this factor is inversely proportional to the shaping time. The electronic noise due to factor (b), on the other hand, is proportional to the shaping time, as is factor (c). Factors (d) and
(e) are generally difficult to predict, which means it is difficult to predict the exact noise performance of a detection system. Fortunately, both of these factors are independent of shaping time, so they have no impact on the determination of the optimal shaping time. In terms of reducing the electronic noise, the optimal shaping time can be predicted by considering only factors (a), (b) and (c). The subject of noise in detection systems using charge sensitive preamplifiers is addressed in more detail in these articles:
_{Bertuccio G; Pullia A; „A Method for the Determination of the Noise Parameters in Preamplifying Systems for Semiconductor Radiation Detectors“, Rev. Sci. Instrum., 64, p. 3294, (1993).
Radeka V; „Low-Noise Techniques in Detectors“, Ann. Rev. Nucl. Part. Sci., 38, p. 217, (1988).
Goulding FS; Landis DA; „Signal Processing for SemiconductorDetectors“, IEEE Trans. Nuc. Sci., NS-29, p. 1125, (1982).}

Output Characteristics
The CR-200 shaping amplifiers have low output impedance (<5Ω) and can source/sink 10 mA of output current. This may not be sufficient to drive a terminated cable in your application, depending on the size of the signal. For this reason it is best to use a cable driver circuit at the CR-200 output to make maximum use of the CR-200 output voltage swing capability. The unloaded output voltage swing comes to within 0.5 volt of the power supply rails.

Electronic Noise (continued)
The following equation can be used to estimate the noise level in a detection system based on the CR-110 charge sensitive preamplifier. Estimates have been made for factors (d) and (e) mentioned previously, assuming short traces on an FR-4 circuit board (such as those found on Cremat's CR-150-AC-C evaluation board). This equation may be useful in allowing the user to calculate the optimal shaping time ( in s) minimizing the electronic noise (ENC in electrons rms) for a given detector capacitance (Cin in pF) and detector leakage current (Id in pA)