Sampler clock and fine delay system for ALMA
                                    M. Torres,  Feb 13th,2003
This paper describes phase-frequency synthesis schemes in an attempt to satisfy all the constraints that have been raised during the last telecon of the sampler clock group on the 4th of February, 2003. It supersedes the previous versions ( 1 , 2 )

Two prototypes have been built January,2004 .  Read the report here.

A preseries for the 8 first ALMA antennas (+ one spare)  has been delivered December,2005.

1. Introduction

It has been found that most of the timing constraints of the Sampler, Demux, and DTX clock signals could be satisfied if the 4 GHz clock was multiplied from the 250 MHz, instead of dividing the 4 GHz down to 250 MHz. Having the dividers inside the PLL is equivalent to multiplying and this provides no phase ambiguity, which is a side effect of out-of-loop division.
However, division has the advantadge of decreasing the size of the phase steps, while increasing their absolute accuracy. On the contrary,  multiplying a 250 MHz signal to 4 GHz also multiplies by the same factor all its imperfections, which are phase noise and phase inaccuracy.

The sampler environment could take the attractive form described below:

This one sounds good

Fig.1 : Clock location in the sampler-related  electronics

Although 8 steps are sufficient, the following designs will aim at 16 steps, because electronics that can offer the required accuracy for the steps are de facto  capable of providing more steps for very little additional cost.

So the engineering problem can be formulated as follows:
- Generate two 250 analog MHz signals, with relative phase  ranging from 0 to 22.50 degrees, in 16 equally spaced steps, 1.40 +/- 0.15 degrees, and then multiply the variable one by 16 so as to obtain a 16-PSK constellation at 4 GHz.

2. Analog solutions
There are several ways of implementing such a phase shift at 250 MHz.

1.  Varactor-tuned resonant circuit-loaded 3dB hybrids.  This solution has been built in series (30 pcs) in an LO3 for the previous generation  PdB correlator (1992). An E2PROM lookup table was needed to correct for their non linearity. A software using the correlator as a phase meter was used to built and upload the lookup table. Although the requirement was quite modest (3 degrees @ 820MHz), they needed frequent recalibration.

2.  Digital timing ICs.  Some all-digital chips make use of many individual gate propagation delays, together with multiplexers, to create substantial programmable delays. As many as 1024 gates can be concatenated. This solution was tested in the lab many years ago but was never applied. The current candidate chip for this task is the Onsemi EP195 . This solution probably does not offer sufficient quality for our application.

3. I/Q modulators.  These chips synthesize a vector of any phase by applying its Cartesian coordinates as voltages on their X and Y inputs. They have the problems that generally affect analog devices, which are drift and non-linearity. Several years ago, a student at IRAM has worked out correction formulae taking into account a non-orthogonal vector basis. This can remove the first-order distorsion quite well but the instability is still present, especially at those 4 points of the circle where zero is applied on X or Y. This is due to the imperfect balance of the Gilbert cells inside the chips. However our application requires that we operate them in a small sector of the circle, and we can take advantadge of this by choosing an operating point where the slope of the actual transfer function is less sensitive to imperfections, e.g. at X=Y= 0.707.

45 degrees is the best place in the house

Fig.2:    I/Q synthesis on a reduced phase range

If the Y (differential) connections are swapped and connected to the X ones, single-dimension operation can result on the tangential (green) segment of Fig.2 . A good 12-bit D-to-A converter, followed by a lookup correction table, can provide adequate resolution and accuracy. Currently available modulators are the Analog Devices AD8345 and Sirenza STQ1016.
Problems associated with this scheme come from the correction tables. They  need to be built up first, and this implies that a more accurate lab equipment setup is available. Tables will need to be personalized, and this is a time-consuming process. It is likely that aging will require further recalibration. On a remote site this might not be practical.

3. Digital solution

    Engineers use to experience a lot of relief when things can go digital. The DDS technique is extremely appropriate for synthesising frequencies and phases. DDS has the inconvenience of generating a fairly high noise floor which in our case would be raised by the multiply-up factor, which is 24 dB. This noise floor is actually pseudo noise that originates in the glitches of the D-to-A converter, which are spread  across extremely long sequences. For some "happy frequencies" which are submultiples of the clock frequency, the sequence repetition length is exactly equal to one cycle of the generated sinewave, so the glitch energy gets tranformed into harmonics rather than pseudonoise.

A convenient frequency setup for generating the two sinewaves we need is Fclock=125 MHz, Fout=Fclock/16.
An analog filter is necessary to convert the staircase wave generated by the D-to A into an unaliased sinewave. In our case it could be a bandpass filter, with a moderate penalty on the overall settling time.
The D-to-A's are clocked at 125 MHz, and receive their data from two lookup tables, which are addressed by two 8-bit registers. Those two registers share the same 4 MSB's which come from a rolling accumulator, which provides the main frequency of 7.8125 MHz. The addition of  LSB's to one of the registers acts as a phase Vernier which has a resolution of 2pi/256 .  Four bits give a total phase excursion of 2pi/16.

''composite DDS'' solution

Fig.3 Functional block diagram of the clock module

The two sinewaves at 7.8125 MHz need to be translated to 250 MHz. Two I/Q modulators are used in an a "shift-up,shift-down" configuration. The AC-coupled use of those chips (opposed to DC-coupled, described above) substantially reduces their two inconvenients:
Drift and aging still occur but the equal spacing of the phase steps is preserved. The absolute value of the delay may vary  slowly, but this will be taken out by calibration on sky sources (e.g. like antenna deformations).
Non-linearity happens to be swept at the AC frequency so the small deviations from the ideal,linear transfer function of the I/Q modulator are exported to an harmonic of this frequency (see annex 1).

With the frequency values of Fig.3, lines can be expected at 258,266,274 MHz... and also 242,234... but they will be filtered by  the x16 PLL with a slope of 12 dB/octave. With 200kHz of loopBW, a delta of 7 MHz is rejected by 60dB.  As long  as the PLL is locked to the "nice and clean" line, it will transfer its accurately synthesized phase variations to the 4 GHz VCO. For the lock-in to be safe, 20 dB spurious ratio is sufficient. This seems to be achievable and reproductible without excesssive development.