*Reza Moghimi*

*EDN*

You need optical-power monitoring to guarantee overall system performance in fiber-optic communication systems. Logarithmic-signal processing can maintain precise measurements over a wide dynamic range. The wide-dynamic-range signal undergoes compression, and the use of a lower resolution measurement system then saves cost. As an example of this technique, consider a photodiode with responsivity of 0.5 A/W that converts light energy to a current of 100 nA to 1 mA. With a four-decade dynamic range and 1% error, the required measurement resolution is 0.01×10^{–4}, or 1 ppm. This measurement requires a 20-bit ADC.

Instead, you can compress this input to a 0 to 4 V range using a log-ratio amplifier and then use a 10-bit ADC, substantially reducing the system cost. Programming the reference current allows shifting the output voltage to the desired level. You can customize and use the circuit in Figure 1 in applications involving unusual combinations of dynamic range; input signal, such as voltage or current; polarity; and scaling; or operations such as log products and ratios.

Figure 1. |
This circuit is a programmable, temperature-compensated log-ratio amplifier. |

Log-ratio amplifiers find applications in wide-dynamic-range ratiometric measurements, which measure an unknown signal against a variable-current reference. The transfer function of the circuit in Figure 1 is:

where K is the output scale factor, I_{IN} is the current that the photodiode generates, V_{T} is a temperature-dependent term (typically, 26 mV at 25 °C and proportional to absolute temperature), and I_{REF} is the reference current. V_{OUT}=0 when I_{IN}=I_{REF}. For proper operation, I_{IN}/I_{REF} should always be greater than 0. The output of the log-ratio circuit can be positive, negative, or bipolar, depending on the ratio of I_{IN}/I_{REF}. The 4 V full-scale input range of the ADC sets the 4-mA full-scale input-current range. Programming I_{REF} to a value of 40 to 600 µA places the output in the middle of the measurement range.

The components give an output-scale factor of –1. This circuit has an output defined over a range of 4.5 decades of signal current, I_{IN}, and 1.5 decades of reference current, I_{REF} (limited by the load-driving capability of the reference for a total six-decade range). For most applications, you would use only a portion of the entire six-decade range. By determining the range of the expected input signals and computing their ratios, you can use the equations to predict the expected output-voltage range. You can assign I_{REF} and I_{IN} to match device performance to the current range, but you should observe polarity.

A log amplifier generally depends on the nonlinear transfer function of a transistor. The general transfer function of a log amplifier is related to I_{S} and V_{T}, which both depend on temperature. I_{S} is the transistor's collector saturation current, and V_{T} is the transistor's "thermal voltage." To overcome this temperature dependency, this design uses a matched pair of MAT02 transistors to cancel the I_{S} temperature drift and a temperature-sensitive resistive voltage divider to compensate for the temperature coefficient of V_{T}. The heart of the I_{REF} generator is a REF191. You adjust its output with an AD5201 digital potentiometer. This modification allows you to program the reference current in 33 steps, from 40 to 600 µA.

Figure 2. |
V_{OUT} has I_{REF }programmed to full scale of 570 µA. |

Figure 3. |
V_{OUT} has I_{REF} programmed to zero scale of 40 µA. |

The combination of the REF191 and the AD5201 provides a current source that is stable with respect to time and temperature. For higher resolution, you can use the 1024-position AD5231. The AD8626 is a dual precision-JFET-input amplifier with true single-supply operation to 26 V, low power consumption, and rail-to-rail output swing, allowing a wide dynamic range. Its output is stable with capacitive loads in excess of 500 pF. Figure 2 and Figure 3 show the transfer function of the log-ratio amplifier at the input of the ADC. The output is limited to 0 to 4 V to match the unipolar input-voltage range of the AD7810 ADC.

- Sheingold, Dan, Editor, Nonlinear Circuits Handbook, Analog Devices, ISBN: 0-916550-01-X.

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