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jcx 16th June 2010 08:13 PM

The Other Hawksford IV (nested loop op amps)
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I found a way to make the sim of Hawksford's nested op amp I/V in the last section of the paper finally work:

people always want to make the discrete I/V but no one discusses the nested loop op amp I/V

adding the RC across the DAC input finally killed the oscillation I've always seen before in sim - clearly there are some constraints hidden in the "pre-filter" box

I juiced up the op amp choices with Lt supplied models - LT1115 is a low noise, fast, unity gain compensated LT1028 speced for audio

I moved the U2 op amp -in connection which seems to give better damping

the sim plots the input error V of the nested and a single LT1115 I/V with a 2 mA 1nS rise step input

the nested topology slightly reduces the peak error but hugely reduces the integrated error (green nested loop, yellow single op amp I/V, inverted response)

abraxalito 17th June 2010 12:17 AM

Nice work. I've been wanting to play with that design for some time now. With your 10R/10n on the input the opamp noise gain is hugely increased, so doesn't it work with non-UGS amps too?

jcx 17th June 2010 03:14 AM

I don't think the noise gain is a problem for audio - the 10 nF * 2.2 KOhm corner is ~7 KHz, if you start multiplying ~ 1nV/sqrt(Hz) from there it won't impact weighted audio S/N

whether its an opportunity is a question - maybe decomp LT1028 or AD797 would work in the front end - personally I'd try the new ADA4898 with the Gilbert multi-tanh input linearization

the U2 op amp needed to be slower as you can see from the ~8 MHz GBW LT1022 there- but I can add local feedback and RC to cancel the zero and use a much hotter op amp in the sim in that position as well - higher output drive should be helpful in addition to allowing better tuning of the dynamics

so far I've just been poking around with the sim - obviously a analysis and design rules for filter pole position, stability would be good

- does seem to work with the "not exactly unity gain stable" LT1028 in U1 position

abraxalito 17th June 2010 04:18 AM

For the past several months, I've been attempting to correlate listening impressions with sim results. No joy yet. What I've found empirically is my ears prefer a smaller feedback capacitance (500pF that you have here being too big - ambient acoustics get lost somehow). But there is a limit to how small it can go with a particular opamp before it starts sounding really terrible - the wider bandwidth/high slew rate opamps can tolerate much lower values. I'm using the LM6172 at the moment which works with no cap at all but sounds just a tad zingy.

I hadn't twigged that the ADA4898 had the Gilbert input stage, it just says 'proprietary' in the DS. I'd ruled that one out for I/V on the basis of its fairly horrid settling performance. However there's good reason to believe its only that bad at G=1, the higher gain small signal pulses look much cleaner. So I'll put this one on my mental list of opamps to try out, thanks.

Nazar_lv 17th June 2010 08:50 AM

jcx 17th June 2010 07:19 PM


Originally Posted by abraxalito (
... What I've found empirically is my ears prefer a smaller feedback capacitance (500pF that you have here being too big - ambient acoustics get lost somehow)...

single pole is "droopy" and its possible stringing too many even >100 KHz 1st order poles will eventually have a effect on audio highs

Hawksford's nested op amp I/V is a 2nd order ~ Butterworth - I would always recommend designing in maximally flat filter responses, matching up any single pole with higher Q biquad sections to prevent audio frequency roll off

in sim, and likely real life the U3 unity buffer seems to limit audio frequency linearity - full signal common mode V causes input distortion with 6K source resistance

jcx 5th July 2010 06:10 PM

a little more circuit sim...
2 Attachment(s)
working towards a better implementation of the Hawksford nested loop I/V I’ve added a few tricks to the basic circuit

I impedance scaled the 1st post’s circuit values to be more appropriate for the PCM1794 under discussion in another thread

U1 op amp is the error summer for the whole loop – input linearity is paramount, intrinsic op amp input diff pair stage linearity and keeping error V low are the available tools

The ADA4898 is a new option for low V noise, extended input linearity with speed and high “linear output current”; definitely 1st choice on tech specs for U1 position – the sim uses LT1028 due to the unavailability of a ADA4898 spice model

The “noise gain” shunt R6,C5 can passively soak up some of the fast edge from the DAC – limited by the requirement for damping R8 and component/layout parasitic esl

At DAC switching glitch edge frequencies C1 (smt NP0/C0G) shorts the input to the U1 op amp output – creating fast rising current demand from the U1 output – indicating a need for fast op amp, possible Class A bias, or composite with extra buffer in loop – I choose a fast op amp for the sim

the Hawksford circuit’s additional gain loop reduces the error V at U1 input after a few 100 nS by adding current to the summing node through C2,3,4 and finally for audio frequencies the feedback R, R3

U1 output doesn’t swing more than 10s of mV so U1 can run at reduced supply V for lower self-heating and noise – local subregulated supplies for U1 are a practical audiophile tweak with possible benefits

again at high frequencies “C2” shorts the input to the U2 op amp output so the same op amp output impedance concerns apply as for U1 – but U2 needs to be slower for overall I/V circuit stability – I choose to use local feedback giving high frequency integrator response to allow a faster op amp to be used here in hopes that a high speed U2 op amp will have lower output Z, the sim shows U2 output current demand peaking @~150% the DAC input delta I step – simmed with fast LT1028 op amp

“C2” is a passive composite – C2b,c are the high speed path and these caps should be smt NP0/C0G
R14 shunts audio frequencies possibly distorted by C2b

the lower frequency signals pass thru C2a which can be a polystyrene wound foil type – which has excellent audio distortion properties but too much esl for the job of soaking up fast DAC edges

C3,4 also handle “slow” signals due to the series R1,2 and can be wound foil polystyrene

“U3” follower errors can limit the linearity of the circuit – so a composite is used in this position – by balancing the source/feedback impedance the nonlinear common mode input Z errors of FET input op amps are avoided, then the modified integrator U4 CFA amp inside the U3 feedback loop buffers the output load and provides high audio frequency loop gain, U3’s FET input diff pair is presumably more immune to the remaining feedthrough V spikes than a bjt diff pair – U3 LT1022 FET input op amp used in the sim is broadly similar to the popular OPA132/4 series

U4 provides gain and output buffering inside the U3 unity feedback loop - the sim's LT1497 is one of Linear's A/DSL driver CFA op amps

while many real op amp distortion generating mechanisms are not properly simulated some input stage and loop gain related issues are – with the measures taken the sim shows ~ -130 dB 2nd harmonic distortion, decreasing higher harmonics with “mono” PCM1794 DAC 20KHz full scale signal level

jcx 4th September 2012 06:03 PM

2 Attachment(s)
In response to some PM interest I'm posting a simpler 2 op amp nested I/V I hacked out of the earlier Hawksford nested feedback multiloop I/V sim

I am not as knowledgeable on these circuits as I'd like to be before posting circuits but I have lucked on a few configurations that appear to work in sim

I believe Hawksford is drawing inspiration from higher order Sigma-Delta converter noise shaping filters - I would look in that field's literature for guidance on these nested feedback topologies, their design equations for stability, transfer functions

below a fast (90 MHz GBW) input op amp is supplemented with a diamond buffer – mostly because I don't believe the Spice macromodel's output - many just use controlled ideal source connected to gnd internally

“noise gain” input shunting series RC, fast input op amp, heavy local C feedback are attempts to minimize the input delta V, magnitude*time product as a quality measure

the slower output op amp drives the outer feedback R || C giving a higher order response, reducing the input error transient duration vs the single fast op amp sim to the left added for comparison

clearly there are some stability conditions on relative op amp GBW, input, nested feedback component values - which I haven't worked out – I'm just playing around, inspired by Hawkford's example circuit

the “figure of merit” I am using is the input error transient, |magnitude|*time product – I've added a pair of BV to calculate the input transient absolute value time integral – the 2 op amp nested circuit improves this number by ~ 20x

Sebastiaan 27th November 2012 01:37 PM

Dear JCX,

Try to sim a simple I-V convertor with just the old school NE5534. In my SIM. This hated Op Amp shows an almost perfect impulse response with a 1nS. step pulse.

Why this is I have no clue...

With kind regards,

Sebastiaan 29th November 2012 10:32 AM

Please see here:

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