# Doing the math on HP5065A¶

A very relevant question at this point in my project is how good a the C-field constant current driver needs to be. Lets do the math:

The C-field current varies from 2.5 {mA} to 6.5 {mA} when the C-field pot is turned from one extreme to the other.

This full range of the pot is a frequency change of 2e-9 {s/s}.

It’s not a straight line curve, but if we pretend it is, we get a sensitivity of:

```2e-9 {s/s} / (6.5e-3 {A} - 2.5e-3 {A}) = 5e-7 {1/A}
```

The performance of Corby Dawsons “Super 5065A” levels out at 4e-14 {s/s}, and there is no reason to belive that is the limit, so lets aim for a C-field noise contribution of 1e-14 {s/s}:

```1e-14 {s/s} / 5e-7 {1/A} = 2e-8 {A} = 20 {nA}
```

If we use a 10 {V} reference, the current sense resistor must be 760 {Ohm}, to make 250 on the pot dial correspond to 4 {mA} current.

The noise voltage across the resistor must be less than:

```760 {Ohm} * 20 {nA} = 15 {µV}
```

The total voltage over the current sense resistor is between 1.9 {V} and 5 {V}, taking the worst case, the noise voltage on the 10 {V} reference can be up to:

```10 {V} / 5.0 {V} * 15 {µV} = 30 {µV}
```

Which corresponds to:

```30 {uV} / 10 {V} = 3 {PPM}
```

## Is that even possible ?¶

The 3 {PPM} spec is a tough row to hoe, because that assumes perfect components throughout the rest of the circuit.

Measurements on my HP5065A indicates a tempco up to 20 {PPM/K} for the C-field pot, with the very typical segmented “strange” curve of mechanical devices.

I have not found any pots which had significantly tighter specification than that, when used in “rheostat” mode.

So the C-field pot has to go.

Now the frequency is no longer tunable.

In my case that is not important, my need is a stable reference source to measure other sources stability against, so it doesn’t matter if the frequency is a little bit off - in fact it is a good thing since that averages various noise sources out over time.

One way to tune the frequency would be to put a 48 bit DDS on the output, and have that emit whatever frequency is desired.

A minor issue is that the adjustment procedures calls for three different C-field pot values: 200, 250 & 300.

This corresponds to voltage divider ratios of:

```(200 {Ohm} + 333 {Ohm}) / (1333 {Ohm} + 200 {Ohm} + 333 {Ohm}) = 0.286
(250 {Ohm} + 333 {Ohm}) / (1333 {Ohm} + 250 {Ohm} + 333 {Ohm}) = 0.304
(300 {Ohm} + 333 {Ohm}) / (1333 {Ohm} + 300 {Ohm} + 333 {Ohm}) = 0.322
```

Which again corresponds to currents of:

```10 {V} * 0.286 / 760 {Ohm} = 3.76 {mA}
10 {V} * 0.304 / 760 {Ohm} = 4.00 {mA}
10 {V} * 0.322 / 760 {Ohm} = 4.24 {mA}
```

(Note that this ignores the approx 12 {Ohm} resistance of the C-field solenoid.)

If we use a circuit with a 10 {V} voltage reference, driving the C-field coil through a very stable series resistor, we find the resistor values should be:

```760 {Ohm} / 0.286 = 2657 {Ohm}
760 {Ohm} / 0.304 = 2500 {Ohm}
760 {Ohm} / 0.322 = 2360 {Ohm}
```

2500 {Ohm} is a standard value in high precision resistors, for instance Vishays Z201 series, so that is an obvious choice for “normal”.

Judging from the service manuals text about the adjustment procedure, the two extreme values don’t have to be particular precise, so normal 1% or 0.1% metal film resistors will probably be fine.

Needless to say the switch used to select one of the three resistors must be high quality.

There is some debate about exactly how good Vishay Z201 resistors are and under what circumstances that can happen, but it seems likely that in this case \$40 will buy you a resistor good enough to ignore.

That leaves most of the 3 {PPM} error budget available for the voltage reference IC.

That is feasible, if nothing else by using the ultimate LTZ1000 chip, but doing a quick selection at a distributor website, filtering for output current > 4 {mA}, input voltage > 20 {V} and output voltage 10 {V} reveals a number of candidates:

```AD588           1.5 {PPM/K}
REF102          2.5 {PPM/K}      5 {µVp-p typ}