1 Introduction

The focus of this memo is on how to arrive at a sequence of Local Oscillator settings given a certain sky frequency and a bandwidth.   It is more detailed than the description of the local oscillator chain in Section 2.2 of A guide for VLA Spectral Line observers ed. 9 (Wilcots, Brinks, and Higdon).   This discussion is divided in various sections, each concentrating on mixing the incoming signal to a new frequency that allows the whole band to fit within the allowed range.   Within each section, a detailed description is followed by the constraints the available frequency range imposes on the allowable LO settings.

2 First LO - conversion to C-band

2.1 Description

In the first LO stage, sky frequencies v_f are converted to a frequency v_c that lies in the range 4.5 - 5.0 GHz (C-band).   Exceptions are obviously C-band itself, and P and 4 band.   The latter two are converted directly to the frequency range 1000 - 1050 MHz using the second LO (see Section 3.1.2).

At each antenna, three different Local Oscillators are used for the conversion to C-band: F2, F3, and F12.   These LO's can be tuned as follows:

The following table shows the conversion from sky frequency v_f to C-band frequency v_c.   For most bands, after mixing, the upper side band (USB) is used; in that case v_f carries a + sign.   X and U band use lower sideband (LSB); hence the - sign.

2.2 Constraints

Of all possible combination of LO settings, one needs to select those that allow the observed band to fall within the range 4.5 - 5.0 GHz.   Since band edges (4% of the total band at each end) tend to be unusable, we only need to fit the central 92% of the total bandwidth B.   So the LO settings have to satisfy the following two constraints:

A special constraint exists for F3.   For this LO, it is advisable to choose n>=5 in the table above.   For n <=4 (15.5 GHz <= F3 <= 16.9 GHz) the LO may not lock.

3 Second LO - conversion to 1000 - 1050 MHz

3.1   Description

3.1.1.   All bands except P and 4

At this stage, a second LO (L6) is used to convert v_c further down to fall within the 1000 - 1050 MHz range, also known as the 1 GHz band.   For all bands except P and 4 band, the 1 GHz frequency v_w is related to v_c by:

The L6 frequencies can be tuned as follows:

3.1.2  P and 4 band

In two cases in the above table, n can be allowed to run starting at 0 instead of at 12.   The first case is non-standard observing, when the user intends to observe frequencies normally not in a supported band. A second case is 4 or P band, when the L6 frequency is mixed with either 2400 MHz or 3000 MHz, and the resulting frequency is used to bring the 4 or P band frequency directly in the 1 GHz band.   This auxiliary frequency L6A is given by:

For P band, the L6A frequency usually becomes 689.9 MHz or 710.1 MHz; for 4 Band, 910.1 MHz or 939.9 MHz.   For both bands, the following relation holds for the 1 GHz band frequency v_w:

v_w = v_f - L6A

which is equivalent to (1), with v_f replacing v_c, and L6A replacing L6.

3.2   Constraints

As in the case of the first LO, one needs to select LO settings that allow the full extent of the observed band to fall within the available range.   Unlike in the case of the first LO, this range is not a fixed one, but depends on the user's choice of one of three front-end filters, of widths 50, 25, and 12 MHz respectively.   The narrower the choice of the filter, the smaller the probability that the bandwidth will fit within the filter boundaries v_lo and v_hi.   These, and other properties of the filters are listed in the following table.

The constraints to be applied become:

4    Conversion to baseband; fluke frequencies

4.1    Description

To differentiate between the signals from the four IFs all coming down the waveguide, a different offset frequency v_A is added to each IF, according to the following table. Once in the control building, these signals are mixed with another LO at frequency v_D. This is a 1200 MHz signal for IFs A and B, and a 1800 MHz signal for IFs C and D. The resulting frequency v_r = v_w + v_A - v_D.  For example, for IF A, v_r = v_w - 900.

Finally, the fluke synthesizers will convert v_r further down to baseband, i.e. from 0 to B MHz where B is the total bandwidth.   So the fluke synthesizers will have to be tuned to v_r - v_B, where v_B is the offset frequency to the middle of the band.   Normally, v_B is one-half the filter width (but not for bandwidth codes 8 and 9, see table 2.4 in A Guide for VLA Spectral Line Observers.   Note that - unlike the LO's discussed before - the fluke synthesizers are not restricted to a limited number of frequencies but allow virtually continuous tuning.

4.2    Constraints

4.2.1    100 MHz lower fluke limit

The fluke frequency (for IF A) cannot be smaller than 100 MHz.   In spite of constraints at previous mixing stages, flukes below 100 MHz would still be possible since the v_B used in calculating the fluke frequency is usually 0.50 B, slightly greater than the effective half-bandwidth 0.46 B.   LO setting combinations with the fluke frequency for IF A below 100 MHz need to be discarded.   There is an exception to this; see the following paragraphs for a description.

4.2.2.    A special case - 50 MHz total bandwidth

An interesting problem arises when the total bandwidth is 50 MHz, identical to the total frequency range available for the various intermediate frequencies.   Unless the observing frequency is chosen carefully, the total bandwidth will not easily fit within the allowable range.   Since the effective bandwidth is only 46 MHz (92% of 50MHz), we do have some leeway, but it may be necessary to relax the condition that 100 MHz be the lower limit for the IF A fluke frequency.

For example, if the sky frequency at L-band is 1413.1 MHz, using the fixed L2 at 3.2 GHz and L6 at 3589.9 MHz, v_w becomes 1023.2 MHz, which allows the bandwidth, running from 1000.2 MHz to 1046.2 MHz, to just fit within the allowed limits.   The fluke for IF A will have to be tuned at 123.2 MHz minus the 25 MHz baseband offset, resulting in 98.2 MHz.   Under these special circumstances, this low fluke setting should be allowed, but not without warning the user, and suggesting that better results can be expected by choosing a sky frequency which is higher by 1.8 MHz.   The spacing between these ideal frequencies is determined by the 20 or 30 MHz interval between the possible L6 settings.

5    IF considerations and constraints

So far, the discussion has been largely independent of the two IF pairs, AC and BD.   However, the IF pairs are not independent since both share the first LO: F2, F3, or F12 (whichever applies) has to be the same for both IF pairs.   So, at this stage, any LO combination in which the first LO setting for AC is different from that of BD has to be discarded.   In Q-band, which uses two different first LO's, both have to be identical for AC and BD. If this condition should eliminate all LO combinations, this means that the requested sky frequencies for the two IF pairs are too far apart.

The second LO provides independent tuning for AC and BD, and no such constraint applies at this stage.

6    Optimizing the choice of LO's

The VLA LO system has a certain amount of redundancy, which in some cases leads to various possible combinations of the different LO's for one given sky frequency.   This section describes how to make an optimal choice if more than one option presents itself.

6.1   Position of band within allowed range

Any LO setting with v_c in the 4.5 - 4.0 GHz range and with v_w in the 1000 - 1050 MHz range is viable.   It is advisable, though, to select the setting that causes v_w as much as possible in the middle of the allowable range, even if that would place v_c more towards the edge of its allowable range.

All fluke settings within the range 100 - 150 MHz should be equally good; the various possibilities therefore can be ranked entirely based on how centrally the band centered on v_w lies in the 1000 - 1050 MHz range.   The only other constraint that applies here is the possible presence of interference at certain intermediate frequencies, the so-called birdies.

6.2    Birdies

Birdies show up at multiples of 600 MHz.   This mainly affects 4800 MHz in C-band.   Given more than one setting for the first LO, the one that causes 4800 MHz to fall within the band centered on v_c should be discarded.   If this is the only choice available, the user should be clearly warned about this.

In Q-band, the first intermediate frequency is at 3F3 - v_f GHz.   At this intermediate frequency, any setting of F3 that causes 4.8 GHz to fall within the band should be avoided.   Since the values of 3F3 are so coarsely spaced it may not always be possible to avoid this frequency.

Author:  Gustaaf van Moorsel

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