The Cosmic Background Imager: Correlator

Cross-correlating 10-GHz bandwidth signals from 13 antennas is a large computational problem. A digital approach is too expensive for a small instrument, so the CBI uses an analog filter-bank correlator. Signals from each receiver are split into ten 1-GHz wide bands in a bank of microwave filters. Each band is downconverted to 1-2 GHz and then fed into an array of complex multipliers which compute the real and imaginary parts of the cross-correlation. The main difficulty in such a system is distributing signals to all the multipliers without adding large passband errors which degrade the sensitivity. In the CBI, all the multipliers for one band are integrated into a single compact circuit. The multipliers are arranged on a square grid in two triangular arrays. The upper right array computes the real part of the cross-correlations and the lower left array computes the imaginary part. Signals from the antennas pass along the square grid of microstrip transmission lines and there is a Gilbert Cell multiplier at each intersection. The Gilbert Cell multipliers have a bandwidth of ~ 5 GHz, so the passband errors in the 1-2 GHz band are small. This type of multiplier is also quite sensitive (~ 50 mV output with -20 dBm inputs) so the noise contribution of the post-multiplier electronics is negligible. The quadrature channels in the CBI correlator are generated by lumped-element hybrids and the prototype unit has peak quadrature errors of ~ 7° at the band edges and typical errors of ~ 3° over most of the band. All the microwave components are chip devices with wire-bonded connections. This makes the correlator compact and helps to minimize passband errors due to reflections.

Detail of part of the correlator assembly showing microstrip transmission lines and Gilbert Cell multipliers.

Schematic of a portion of the correlator showing the square grid of microstrip transmission lines and multipliers at each intersection, plus details of the individual cells.

A correlator board. This performs the cross-correlation of 78 baselines for a single 1-GHz channel. The microstrip transmission lines and Gilbert Cell multipliers are housed in the box at right, which is shown open below.

The output of each multiplier in the correlator is integrated for 12.8 ľs, which is the basic state time of the 180° phase switch applied to the first local oscillator in the receivers. The signals are then digitized with 16-bit resolution and further integrated for 0.8 s in a digital accumulator which also demodulates the 180° phase switch. The fast phase switch removes offsets and any slowly varying unwanted signals such as power-line pickup.

The entire correlator occupies about a 30-cm cube and is attached to the back of the antenna platform along with all the other control electronics. This makes the antenna and electronics assembly a single rigid structure and avoids the instabilities introduced by moving cables. Stability is particularly important for an instrument with an analog correlator because the multiplier gains and quadrature errors must be calibrated regularly. In the CBI this is done by injecting correlated wide-band noise at the input of each receiver. The calibration signals are sent to each antenna via stable cables in a constant temperature environment and the noise generator is continuously monitored by a power meter. Each receiver local oscillator has an accurate 90° phase switch to allow measurements of the correlator quadrature errors. The fundamental amplitude calibration for the CBI is based on observations of planets, but the noise calibration scheme is used to improve the stability of the instrument between these observations.