The Local Oscillator Chain

Converting the sky frequency to another frequency is done because it is more attractive to carry out such tasks as filtering, delaying, and cross-correlating the signal at a fixed frequency different from the sky frequency, ${\nu}_{RF}$ (where RF stands for Radio Frequency). This also allows the system to be optimized, having minimum redundancy between bands. It is achieved by mixing the incoming signal, ${\nu}_{in}$, with that of a single-valued local oscillator (LO) frequency, ${\nu}_{LO}$, giving an intermediate frequency, $\nu_{IF}$, such that $\nu_{in}=\nu_{LO}\pm\nu_{IF}$. The plus sign indicates the ``upper'' sideband and the minus sign indicates the ``lower'' sideband. All of the mixers at the VLA are single sideband mixers which means that only one product (e.g., the upper sideband) is amplified and eventually sent to the correlator while the other is rejected. We will, at times, refer to some of the hardware used in the VLA for frequency conversion; for example, the ``L6 frequency synthesizers'' and ``F12 Frequency Converter''. Of particular importance are the first LO (${\nu}_{1}$), the L6 (${\nu}_{L6}$) and the Fluke synthesizers (${\nu}_{f}$). The following table cross-references the items discussed here with their alternative designations found in the observe program. Note that the 3.2 GHz, 12-15 GHz, and 17-20 GHz LOs all act as ``first LOs'' for the bands to which they apply.

Table 2.1: LO Chain Nomenclature
Terminology	Label	observe	Function
``F3''	17-20 GHz LO	``Front-End LO''	converts U, K-bands
			to 4.5-5.0 GHz
``F12''	12-15 GHz LO	``Front-End LO''	converts Q, X-bands
			to 4.5-5.0 GHz
``F2''	3.2 GHz LO	``Front-End LO''	converts L-band to
			to 4.5-5.0 GHz
``L6''	2-4 GHz LO	``2-4 GHz LO''	mixed with 4.5-5.0 GHz signal
			to yield 1000-1050 MHz signal
			also produces auxiliary 690 MHz
			signal to convert P-band to
			1000-1050 MHz

An overview of the LO system is shown in Figure 2.2 where we schematically trace the signal path for each of the bands. The circles containing an ``X'' indicate where the incoming signal is mixed with the signal from a local oscillator. The ovals marked with an ``S'' indicate a band switch, a device to select between the various front-end signals. The signal path is traced by the solid lines while the LO signal is traced by the dashed lines.

K-Band (1.3 cm), U-Band (2.0 cm): The first LO frequencies for these bands are set between 17.0 and 20.0 GHz satisfying the following condition:

$$\nu_{LO}=17.1+(n\times0.3)\pm0.1~{\rm GHz}.$$ (2.1)

This LO signal is mixed with the incoming sky frequency; K-band uses the upper and U-band the lower sideband. The resultant signal (which is in the range of 4.5-5.0 GHz) is then mixed into the range of 1000-1050 MHz using the L6 frequency synthesizer. This can be tuned to any frequency between 2010 and 4010 MHz in alternating steps of 20 and 30 MHz (e.g. 2010, 2040, 2060, ...MHz). Once the signal is mixed with $\nu_{L6}$ it is ready to be transmitted to the waveguide and control building.

Q-Band (7 mm), X-Band (3.6 cm): The first LO at Q-band is the same as the one used at K and U-bands. The difference is that at Q-band this first LO is tripled (marked with an ``x3'' in Figure 2.2) and is then mixed with the incoming signal. The effect of this mixing is to downconvert the Q-band signal to X-band. The value of this first (tripled) LO is held within the range of 50.1 to 61.8 GHz in alternating steps of 0.3 and 0.6 GHz (i.e., 50.1, 50.4, 51.0, ...GHz). The resulting signal is then mixed into the range of 4.5-5.0 GHz using the F12 frequency converter which is shared with X-band. This LO is held at either 12.8, 13.0 or 13.4 GHz. After further amplification the signal is converted down by the L6 frequency synthesizers into the range 1000-1050 MHz.

C-Band (6 cm): The incoming C-band signal undergoes initial amplification and is then sent directly to be mixed with the L6 frequency synthesizers.

L-Band (20 cm): The incoming 20 cm signal is initially upconverted with a first LO set to 3.2 GHz, and the resulting signal is converted by the L6 frequency synthesizers as detailed above. This first LO is fixed for L-band.

P-Band (90 cm): The P-band signal follows a slightly different course; its incoming signal is mixed directly into the range of 1000-1050 MHz utilizing an LO set at 690 MHz. This is provided by the L6 frequency synthesizer which, in addition to its normal output, also produces an auxiliary output at 690 MHz.

Following these initial steps, which have brought the incoming signals into the range of 1000-1050 MHz, all bands are now treated in an identical manner. The resulting signals for each IF are mixed with an offset frequency (${\nu}_{A}$) to get them into the range of 1200-1800 MHz for transmission through the waveguide system. The offset frequencies and the resulting bands for each IF are listed below:

Table 2.2: Offset Frequencies
IF	${\nu}_{A}$	Wave Guide Band
A	300 MHz	1300-1350 MHz
B	400 MHz	1400-1450 MHz
C	550 MHz	1550-1600 MHz
D	650 MHz	1650-1700 MHz

The signals in the frequency range listed in column 3 in Table 2.2 above are then mixed with an LO at frequency $\nu_{D}$ in the control building. This is a 1200 MHz signal for IFs A and B and an 1800 MHz one for IFs C and D. The resulting signals are found in the ranges given in column [2] of Table 2.2. The minus sign is used to signify that the ``lower'' sideband is used in this mixing.

The signal is further mixed with a ``Fluke'' frequency, $\nu_{f}$, which is used to convert it to baseband (i.e., frequency running from 0 to B MHz where B is the bandwidth of the baseband filter). The purpose of this mixing is to choose part of the incoming signal which has a bandwidth of 50 MHz (column [2] of Table 2.2) to be filtered and passed to the sampler. $\nu_{f}$ is therefore a frequency that falls within the incoming 50 MHz range with the formalism as listed in the third column of Table 2.3.

Table 2.3: Fluke Frequencies
IF	Range	``Fluke'' frequency
A	100 to 150 MHz	$\nu_{f}$(A)
B	200 to 250 MHz	$\nu_{f}$(B)/2
C	$-250$ to $-200$ MHz	$-\nu_{f}$(C)/2
D	$-150$ to $-100$ MHz	$-\nu_{f}$(D)

To facilitate polarization measurements, the AC and BD ``Flukes'' are locked such that $\nu_{f}(A)-\nu_{f}(C)=350~{\rm MHz}$ and $\nu_{f}(B)-\nu_{f}(D)=350~{\rm MHz}$. Finally, the signal goes through the baseband filters. The width of these filters corresponds to the bandwidth selected for the observation (see column [3] in Table 2.4 or column [2] in the tables in Appendix A). To obtain the central observing frequency, one must add an offset frequency, $\nu_{B}$, (typically, one-half of the filter width) to the ``sum of LOs''. The baseband frequency offset and bandwidths are listed in Table 2.4 as a function of bandwidth code.

Table 2.4: Baseband Frequencies & Bandwidths
Bandwidth Code	$\nu_{B}$(MHz)	Bandwidth (MHz)
0	25	50
1	12.5	25
2	6.25	12.5
3	3.125	6.25
4	1.5625	3.125
5	0.78125	1.5625
6	0.390625	0.78125
8	0.29296875	0.1953125
9	0.29296875	0.1953125

Bandwidth codes 0 through 6 (50 to 0.78 MHz) use low-pass filters, frequencies above the cut-off being filtered out. Bandwidth code 8 uses a bandpass filter that transmits frequencies between 200 and 400 kHz. The offset of the center frequency from baseband is three quarters of the nominal range and only the upper half of this frequency range is usable. Bandwidth code 9 uses the same filter and offset. The filters are designed such that they have a flat response across the inner 75% of their nominal bandwidth. The ``edges'' are steep and should be discarded.

To summarize, the sky frequency relates to the LO frequencies in the following way:

$$\nu_{RF} =\nu_{0}+\nu_{1}{\pm}(\nu_{L6}-\nu_{A}+\nu_{D}+\nu_{f}+\nu_{B})$$ (2.2)

The minus sign is needed for U band and X band and the plus sign for all others. $\nu_{0}$ is 0.0 for all bands except for Q-band where it is the tripled first LO discussed previously. The first LO, $\nu_{1}$, is tunable according to the system which was detailed above for each band; it is fixed at 3.2 GHz at L-band and 0.0 GHz at C and P bands. $\nu_{L6}$ is tunable between 2010 and 4010 MHz (note that $\nu_{L6}=690$ MHz for P-band), and $\nu_{A}$, $\nu_{D}$, $\nu_{f}$, and the baseband frequency offset, $\nu_{B}$, are listed in the tables.

Qualitatively, one can think of the LO chain as a series of steps taken to get the system operating at the particular frequency of choice. Coarse frequency selection is done with the first LO, while further selection is done with the L6 synthesizers. The fine tuning is done in the conversion to baseband carried out by the Fluke synthesizers.