.. _hp5065_c_driver2:

C-field driver - again
=======================

After some work I have designed at this C-field driver:

.. image:: A15_cfld.svg

The main change since :ref:`first version <hp5065_c_driver>` a
couple of extra resistors supply the stable current for the buried
zener in the LM399 voltage reference.

I've run a monte-carlo analysis for the tempco of the components
over a ±10 {K} temperature range.

VCC & R4
--------

VCC is the +20V regulated supply, which I allowed to vary ±0.5 {V}

If R4 is 1M with 100 {ppm/K} tempco, the frequency noise is 6.5e-17 {s/s}.

If R4 is 100k with 100 {ppm/K} tempco, the frequency noise is 5.7e-16 {s/s}.

I have not checked how small R4 needs to be to ensure startup, but
given the low offset voltage of U1, I don't expect problems.

R2 & R3
-------

The voltage over these is the same (± U1's Vos) and their ratio sets the
U2 zener current relative to the C-field current.

With 50 {ppm/K} each of them contributes 6.7e-17 {s/s} frequency noise.

U1
--

LT1007 has a guaranteed max drift with temperature of 0.6 {µV/K}, which
contributes 1.1e-15 {s/s} frequency noise.

There is no need to trim the offset of U1.


R1 & U2
-------

R1 is a Vishay Z201 with a *typical* tempco of ±0.2 {ppm/K}

U2 is a LM399 (without -A suffix) with a *typical* tempco 0.3 {ppm/K}

If we use these typical tempcos, the frequency noise is 4.3e-15 {s/s}

If we use the max tempco, 2 {ppm/K}, for the LM399 and the typical for R1,
the noise rises to 2.4e-14 which is above my 1e-14 {s/s} goal.

There is no max tempco specified for the Z201, and the datasheet
doesn't give me high confidence that the typical is very typical
after all.

Temperature
-----------

The limiting factor is R1 and U2, and all in all there is about 1.5
{ppm/K} tempco to share between them.

Of course ±10 {K} is a pretty brutal condition for a device which
presumably lives in a somewhat civilized laboratory.

If we can keep the excursions to ±2{K}, then R1 can have 3 {ppm/K}
tempco and still stay below target.

Tunable C-field current
-----------------------

Mechanical trimmers have two digit tempcos, and since they
would go between U2 and U1, math isn't even necessary.

A digital solution *may* be possible, there are special DACs for
driving 4-20 {mA} industrial circuits, for instance Analog's AD5422,
which could possibly be beaten into submission, given a good
external reference.

That would be neat, since it would open the way for a GPS discipline
implementation, but that is a project for another day.

Right now I just want to get the Fluke 732A and the long wire out
of the picture.

Monte-Carlo Code
----------------

Here is my monte-carlo simulation in python::

    #!/usr/bin/env python
    # 
    # 
    # VCC 
    #  |
    #  |
    # R4 
    #  |              |\
    #  *--------------| \
    #  |              |  >--- L1 --+
    #  |           +--| /          |
    #  |           |  |/           |
    #  |           |               |
    #  *---- R3 -------+-----------+
    #  |           |   |
    #  |           |  R2
    #  |           |   |
    # D1           +---*
    #  |               |
    #  |              R1
    #  |               |
    # GND             GND
    # 
    
    from __future__ import print_function
    
    import random
    import math
    
    def calc(comp):
    	d = dict(comp)
    	for i in range(5):
    		d["vr1"] = d["D1"] + d["U1"]
    		d["ir1"] = d["vr1"] / d["R1"] 
    		d["vr2"] = d["ir1"] * d["R2"]
    		d["vl1"] = d["ir1"] * d["L1"]
    		d["vout"] = d["vl1"] + d["vr2"] + d["vr1"]
    		d["vr3"] = d["vr1"] + d["vr2"] - d["D1"]
    		d["ir3"] = d["vr3"] / d["R3"]
    		d["ir4"] = (d["VCC"] - d["D1"]) / d["R4"]
    		d["id1"] = d["ir3"] + d["ir4"]
    		d["D1"] = comp["D1"] + d["id1"] * .66
    	return d
    
    def show(d):
    	l = d.keys()
    	l.sort()
    	for i in l:
    		print("%s\t%17.9f" % (i, d[i]))
    
    def ppm(n):
    	r = random.uniform(-n, n)
    	r *= 1e-6
    	r += 1.0
    	return r
    
    comp0 = {
    	"R1":	5000./3,	# Ohm
    	#"R1":	1000.,		# Ohm
    	"R2":	 500,		# Ohm
    	"R3":	2000,		# Ohm
    	"R4":	 1e5,		# Ohm
    	"D1":	   6.9,		# Volt
    	"L1":	  12.0,		# Ohm
    	"U1":	   0.0,		# Volt
    	"VCC":	  20.0,		# Volt
    }
    
    d = calc(comp0)
    show(d)
    iref = d["ir1"]
    
    sy = 0.0
    syy = 0.0
    n = 0.0
    for i in range(1000):
    	x = dict(comp0)
    	dt = 10
    
    	# 2.4e-15 @ 2ppm (LM399), +/- 10K
    	x["D1"] *= ppm(2 * dt)
    
    	# 2.5e-15 @ .2ppm (Z201 TYP!), +/- 10K
    	x["R1"] *= ppm(3.0 * dt)
    
    	# 1.1e-15 @ .6PPM/K (LT1007A), +/- 10K
    	x["U1"] = 1e-6 * random.uniform(-.6 * dt, .6 * dt)
    
    	# 6.7e-17 @ 50pmm, +/- 10K
    	x["R3"] *= ppm(50 * dt)
    
    	# 6.7e-17 @ 50ppm, +/- 10K
    	x["R2"] *= ppm(50 * dt)
    
    	# 6.5e-17 @ 100ppm, +/- 10K, 19.5-20.5 VCC
    	x["VCC"] = random.uniform(19.5, 20.5)
    	x["R4"] *= ppm(100 * dt)
    
    	d = calc(x)
    	df = (d["ir1"] - iref) * 5e-7
    	sy += df
    	syy += df * df
    	n += 1.0
    
    avg = sy / n
    stddev = math.sqrt((syy - sy * sy / n) / (n - 1))
    print("%.1e" % stddev)


*phk*