Influence of resistors in LM399 reference circuit?

[cellularmitosis]

This script can also be used with zeners other than the LM399 (e.g. the 1N829A or 2DW232 zeners).

For example let's say I have a 6.2V 1N829A, I'm willing to consider Vz values up to 2% away from 6.2V, I want an Iz of 7.5mA, I don't want Rf+Rg to exceed 500k, I don't want the current through Rf+Rg to exceed 1mA, and I'd like to use values from the Vishay Dale PTF series of resistors:

Code: [Select]

$ ./bootstrapped-zener-resistors.py vz=6.2 vzerr=0.02 iz=0.0075 maxrfg=500k maxif=0.001 vishay-dale-ptf.txt | column -t -s,
using rfile: vishay-dale-ptf.txt
using vz: 6.2
using vzerr: 0.02
using iz: 0.0075
using maxrfg: 500000.0
using maxif: 0.001
using maxvop: 12.0
biggest vz jump: 0.111
Vz: 6.1290   Vzerr: 1.15%   Vop: 7.0290   Iz(mA): 7.5   If(mA): 0.900   Rz: 120R   Rf: 1K    Rg: 6K81
Vz: 6.2400   Vzerr: 0.65%   Vop: 7.7400   Iz(mA): 7.5   If(mA): 0.020   Rz: 200R   Rf: 75K   Rg: 312K
Vz: 6.3000   Vzerr: 1.61%   Vop: 7.2000   Iz(mA): 7.5   If(mA): 0.600   Rz: 120R   Rf: 1K5   Rg: 10K5

Only three choices available under those criteria!

[cellularmitosis]

I don't know why it took me this long to realize this, but I just realized that the zener resistor value plays a large role in determining the error "attenuation" factor of this circuit.



"Rz" in the above circuit was given as 1k.  This is what turns 1mV of op amp voltage error into 1uA of zener current error.

If you instead used 2k for Rz (and for Rf), 1mV of op amp voltage error becomes 0.5uA of zener current error.

So, if you have some additional voltage headroom on your op amp, you can increase this value a bit to get some additional error attenuation.

This isn't so important with the LM399, because it already has a low output impedance (of about 1R).  However, for other zeners (like the 2DW232) which have higher output impedance, they won't have as good attenuation in this circuit.  Here, using higher value resistors for Rz and Rf would help improve their attenuation.

For example, if you had a 15V Vcc for your op amp, and it can safely swing the output up to 12V, you could use 5k for Rz and Rf for additional error attenuation.

[Cerebus]

For example, if you had a 15V Vcc for your op amp, and it can safely swing the output up to 12V, you could use 5k for Rz and Rf for additional error attenuation.

The values of Rz and Rf are only coupled by the voltage across them, you could have completely different currents going down the divider and zener arms, and hence completely different values for Rf and Rz. I'd opt for putting as much current as I dared down the divider arm to minimize the values of Rf and Rg, thereby reducing their Johnson noise contribution and contribution from the OPA's input current noise. What's acceptable in noise terms from that combination is obviously going to be determined by the OPA noise and zener noise. I suspect that most zeners would be noisy enough that you wouldn't have to be too fussy, but it's worth a quick calculation to get the best performance one can. Obviously too high a current draw from the OPA would be a "bad thing^TM".

[cellularmitosis]

For example, if you had a 15V Vcc for your op amp, and it can safely swing the output up to 12V, you could use 5k for Rz and Rf for additional error attenuation.

The values of Rz and Rf are only coupled by the voltage across them, you could have completely different currents going down the divider and zener arms, and hence completely different values for Rf and Rz. I'd opt for putting as much current as I dared down the divider arm to minimize the values of Rf and Rg, thereby reducing their Johnson noise contribution and contribution from the OPA's input current noise. What's acceptable in noise terms from that combination is obviously going to be determined by the OPA noise and zener noise. I suspect that most zeners would be noisy enough that you wouldn't have to be too fussy, but it's worth a quick calculation to get the best performance one can. Obviously too high a current draw from the OPA would be a "bad thing^TM".

Good point, and I was recently thinking about this when trying to decide what resistors to use for Rf and Rg.  1mA seems high for that branch, but 10k/68k might be a bit on the high side (as you say, johnson noise could become a factor, but also, the circuit becomes more affected by leakage currents, and I would imagine EMI-induced currents have a larger effect).  Interesting that the LT app note "portable calibrator" circuit is somewhere in the middle, in terms of total resistance in that branch (8.8k + 19k + 3k trim).

[MiDi]

I don't know why it took me this long to realize this, but I just realized that the zener resistor value plays a large role in determining the error "attenuation" factor of this circuit.



"Rz" in the above circuit was given as 1k.  This is what turns 1mV of op amp voltage error into 1uA of zener current error.

If you instead used 2k for Rz (and for Rf), 1mV of op amp voltage error becomes 0.5uA of zener current error.

So, if you have some additional voltage headroom on your op amp, you can increase this value a bit to get some additional error attenuation.

This isn't so important with the LM399, because it already has a low output impedance (of about 1R).  However, for other zeners (like the 2DW232) which have higher output impedance, they won't have as good attenuation in this circuit.  Here, using higher value resistors for Rz and Rf would help improve their attenuation.

For example, if you had a 15V Vcc for your op amp, and it can safely swing the output up to 12V, you could use 5k for Rz and Rf for additional error attenuation.

In addition to that:
The error attenuation is maximized near a gain of 1 and loses significance as gain increases.
This is due to the "1 +" term in the gain equation for non-inverting opamp: gain = 1 + Rf/Rg.
The key parameters of opamps - that have an effect here - are input referred, that means this parameters have to be multiplied by the gain.
Comparison for different Rz @ Iz = 1mA, Vz = 6.95V with gain(Rz) = 1 + (Rz x Iz) / Vz and dIz = (gain x dVin) / Rz, with given dVin = 1mV (opamp tempco, drift, noise ...)
1k => gain = 1.14                       => dIz = 1.1µA
2k => gain = 1.29 (+12% to 1k) => dIz = 0.64µA (-78% to 1k)
4k => gain = 1.58 (+22% to 2k) => dIz = 0.39µA  (-63% to 2k)
8k => gain = 2.15 (+37% to 4k) => dIz = 0.27µA (-46% to 4k)

The conclusion remains:
Rz should be set as high as possible (for given max output voltage of opamp)
to have the least significant influence on Iz from errors in Vout from opamp over temperature/time.
Errors in Vout are resulting from opamp due to tempco, drift, noise, ...

The next question arises:
How do errors from feedback network Rf/Rg due to tempco-match, drift-match, noise (gain-error) contribute to the choice for Rz?
It is easy recognizeable that there is a trade-off/target conflict for this... 

And the final question:
Where is the optimum for Rz in therms of influence for all changes in Vout over temperature/time?

[Andreas]

And the final question:
Where is the optimum for Rz in therms of influence for all changes in Vout over temperature/time?

Hello,

That is a easy answer: 3K for a 10V output.

For a 7V output the chance of tracking for the divider resistors RF/RG
will be somewhat higher if they are of the same value.
So with 2 equal resistors (RF/RG) you will have 6K8 for the Rz.
With 3 equal resistors (10.4V output) Rz will be around 3K3.

My experiences with LM399 near room temperature is that the resistors play nearly no role.
Even a pull up 6K8 to a 14V voltage regulator (LT1763) will do the job.
So you can just use good 0.1% resistors (PTF56 or better) for Rz.
Of course RF/RG is more critical if you want to use a 10V output.

with best regards

Andreas

[GigaJoe]

Rz as definer of current for zener - related to dynamic impedance of zener, delta V (output), delta I ( defined by resistor). for Lm around 0.5 - 1 ohm. roughly , 1Ohm * 1 mA = 1mV.  Changing current to 1mA == 1 mV in output change. you may calculate deviance of resistor value, current,  and change in output zener voltage ....  Then  see how it important ...