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I plan to use the OPA657 as a charge sensitive pre-amplifier for measuring the output from a reverse biased PIN photodiode. I would like to further amplify the signal using a wideband EL5163 opamp. The datasheet for the OPA657 states

Connections to other wideband devices on the board may be made with short direct traces or through onboard transmission lines. For short connections, consider the trace and the input to the next device as a lumped capacitive load. Relatively wide traces (50 mils to 100 mils) should be used, preferably with ground and power planes opened up around them. Estimate the total capacitive load and set RS from the plot of Recommended RS vs Capacitive Load. **Low parasitic capacitive loads (< 5 pF) may not need an RS because the OPA657 is nominally compensated to operate with a 2-pF parasitic load.

The EL5163 has an input capacitance of ~1 pF according to its datasheet. So would a direct connection from OPA output to EL input work without the Rs resistor? How does trace length/width contribute to parasitic capacitance? If the connecting trace is less than 1 cm long, and 1.5 mm wide, how much parasitic capacitance is added?

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A complete implementation of charge sensitive amplifier has a capacitor reset node in the feedback circuit. However, you can see a transimpedance amplifier of the OPA657 datasheet (page 21, Figure 34) as the charge sensitive amplifier: being TIA, it converts photodiode's current of (short) light pulses to opamp's output voltage -- its feedback RC network integrates each pulse into a charge accumulated in the feedback capacitor. A voltage across this capacitor is the opamp output voltage; for a small duty factor, the feedback resistor performs resetting, discharging the capacitor between pulses.

PDTIA

Wideband, High-Sensitivity, Transimpedance Amplifier Diagram of Figure 34 shows a high-gain wideband circuit typical for photodiode applications.

The plot of Recommended RS vs Capacitive Load (Figure 17) of section 11.1 Layout Guidelines, item 4 Connections to other wideband devices, with its recommended values for isolation resistor RS, is for the other OPA657-based circuit, a low-gain broadband amplifier. This low-gain broadband amplifier can be used as a voltage buffer or for the filter implementation. You can see this circuit in the bottom left of Figure 18. Frequency Response vs Capacitive Load, page 10 of the datasheet.

LowGainAMP

The low-gain OPA657-based amplifier output is prone to instability, overshoots, and extended settling times and so requires external frequency compensation. The circuit in Figure 31. Broadband Low-Gain Inverting External Compensation shapes the loop gain for good stability to the gain of 6 dB, –2 V/V. The circuits in Figure 18, as well as in Figures 29 and 30, use the out-of-loop frequency compensation technique, placing an isolation resistor (Rs in Figure 18) at the opamp output outside the feedback loop.

Answering your question: if your "charge sensitive preamplifier" is an integrating amplifier or high gain transimpedance amplifier, it would tolerate capacitive loads as high as 100 pF and even higher and does not require the series isolation resistor RS for stable operation. More general, a high gain configuration does not require external frequency compensation network.

The simulation can help you estimate the limits of amplifier stability in the high-gain configuration:

TIA_Cload

.ac runs:

acCLoad1,100

.tran runs:

tranCLoad1,100

OPA657's spice model can be found in the library OPA657.lib of https://www.ti.com/lit/zip/sbom137 zip archive. You can use this unencoded library, with the olb symbol file, in an PSpice simulation "as is". To use the OPA657 model with an LTspice, you use a component opamp2 of LTspice symbols. To adapt the component pins to OPA657.lib model, permutate the parameters in line 60 of the model

.subckt OPA657 VEE VCC VINM VINP VOUT

with the purpose to agree their order with opamp2's pin arrangement.

The updated line should be

.subckt OPA657 VINP VINM VCC VEE VOUT 

To redress LTspice's grievances about "floating" nodes of current sources GRC and GRA, connect these to ground through 1000G resistors:

after each of lines 571 and 605

GRA  101 102 VALUE = { V(101,102)/1e6 }

insert a line

RA00 102 GNDF 1000G

after line 578

GRC  301 302 VALUE = { V(301,302)/1e6 }

insert a line

RC00 302 GNDF 1000G
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