Measuring the frequency response of an optical receiver is easy if you have a standard reference receiver, a simple test setup, and a network analyzer to perform electrical mismatch corrections.

Your test setup consists of the receiver you want to test, a power meter, and a diode laser modulated by an electrical signal generator (see figure). Start by regulating the test setup with a calibrated reference receiver. Then replace the reference receiver with the receiver you wish to characterize and take another measurement. The ratio of the two measurements is almost all you need.

Taking a closer look, the total response T_{x} measured by the test setup (where x is C for the calibrated reference receiver and U for the unknown receiver) is given by:

T_{x} = (A_{G} M_{GL} R_{L}) (R_{x} M_{xM} R_{M})

A_{G} is the voltage the signal generator would deliver to a 50 Ω load. R_{L} is the response of the laser and relates the laser's input voltage to its optical output. R_{x} is the response of the receiver. It relates the receiver's electrical voltage across a 50 Ω load to its optical input power. Finally, R_{M} is the response of the power meter to a source with 50 Ω impedance.

But what are M_{GL} and M_{xM }? These are "mismatch" terms that account for electrical reflections between the laser and the signal generator, and the receiver and power meter. The problem is that at high frequencies, electrical sources and loads are rarely perfectly matched to 50 Ω. When you connect an electrical source to a load, the actual power transferred is rarely that which the source would deliver to a 50 Ω load. Thus, the result of the measurement depends on both the source and load impedance.

The terms A_{G}, R_{L}, M_{GL}, and R_{M} don't change from measurement to measurement. To find the response R_{U} of an unknown receiver, divide the total measured response T_{U} of the test setup with the unknown receiver by the total measured response T_{C} with the calibrated reference receiver (with response R_{C}). After rearranging the ratio, you get

The mismatch terms M_{UM} for the unknown receiver and M_{CM} for the calibrated receiver are different and don't cancel.

How do you calculate M_{CM} and M_{UM }? If you connect the receiver directly to the power meter, M_{xM} is given by

M_{xM} = | 1Γ_{xR}Γ_{M} |^{-2}

where Γ_{xR} and Γ_{M} are the complex electrical reflection coefficients of the receiver and power meter.^{1} If the receiver is connected to the meter via an interconnecting network (such as a bias tee) with scattering parameters S_{ij} (port 1 on the receiver side), M_{xM} is given by:^{2}

Either way, the procedure is straightforward. You use a calibrated vector network analyzer to measure Γ_{U}, Γ_{C}, and Γ_{M} (and S_{ij} if needed) and plug them into the formulas. The interconnecting network for the standard and unknown receivers can be different. For example, the standard receiver can have a coaxial connector, while the unknown is an on-wafer photodiode with coplanar waveguide wafer probe output. The uncertainty in R_{U} is limited by system noise and the uncertainty in M_{RM}.

You might wonder how a standards laboratory calibrates your standard reference receiver. We use the heterodyne beat between two single-frequency lasers as a standard source, a calibrated microwave power meter, and a procedure similar to that outlined above.^{3} The heterodyne signal provides an optical modulation that can be calculated with low uncertainty from basic physical principles. The National Institute of Standards and Technology offers heterodyne measurement of the response magnitude of a photodiode with precision microwave connectors at 1319 and 850 nm. **oe **

*REFERENCES*

1. *Hewlett-Packard Application Note 64-1A,* 1997.

2. *Hewlett Packard Application Note 154,* April 1972, 9-13.

3. P. D. Hale, C. M. Wang, et al., *J. Lightwave Technol.,* 14 2457-2466 (1996).

*The authors are in the Optoelectronics Division at the National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305. Phone: 303-497-5367; e-mail: *__hale@boulder.nist.gov__. Publication of the U. S. Government; not subject to copyright.