C-multiplier again
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From: John Larkin on 24 May 2010 18:37 On Sun, 23 May 2010 18:01:24 -0700 (PDT), dagmargoodboat(a)yahoo.com wrote: >On May 23, 5:07�pm, John Larkin ><jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: >> On Sun, 23 May 2010 13:26:26 -0700 (PDT), dagmargoodb...(a)yahoo.com >> wrote: >> >> >> >> >On May 23, 11:29�am, John Larkin >> ><jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: >> >> On 23 May 2010 04:28:01 -0700, Winfield Hill >> >> >> <Winfield_mem...(a)newsguy.com> wrote: >> >> >John Larkin wrote... >> >> >> >> I need a super-low noise power supply. I have a 15 volt switching >> >> >> wall-wart input and want as close to 15 volts, regulated, as I can >> >> >> get; 14 would be nice, 13.5 is OK. >> >> >> >> The LDOs that I can find are all pretty noisy and have mediocre PSRR. >> >> >> >> So I thought about using a Phil Hobbs-ian c-multiplier transistor, an >> >> >> R-C lowpass and an emitter follower, with a slow opamp loop wrapped >> >> >> around it for DC regulation. It looks fine on paper, simple loop to >> >> >> stabilize, but I figured I may as well Spice it and be sure. >> >> >> >> What I'm seeing is mediocre PSRR. Stripping out the opamp and such, I >> >> >> have... �ftp://jjlarkin.lmi.net/C-multiplier.gif >> >> >> which has psrr of about 70 dB at low frequencies, improving as the >> >> >> output cap finally kicks in at around 5 KHz. The transistor equivalent >> >> >> seems to look like the expected dynamic Re of about 2 ohms, with a C-E >> >> >> resistor of around 6.6K. Reducing Vb (and Vout) doesn't help much. >> >> >> > You're complaining about a 70dB improvement? �There is a simple >> >> > way to use your 0.7 volts, well maybe 0.8 volts, to get even >> >> > more rejection: change your simple NPN follower into a Sziklai >> >> > connection (AoE page 95). �The base resistor across the added >> >> > PNP creates a relatively-fixed collector current for your NPN, >> >> > which means a fixed Vbe, for improved AC ripple rejection. >> >> >> Since the problem is the Early effect, namely the effective C-E >> >> resistance bleeding ripple through, it didn't seem to me like the >> >> Sziklai thing would help. The PNP doesn't insulate the NPN from the >> >> ripple. So I spiced it. If the LT Spice transistor models are to be >> >> trusted, it's actually worse. The optimum value for the PNP's b-e >> >> resistor is zero. >> >> >> John >> >> >Win's idea looks pretty decent to me, IIUIC: >> >> >FIG. 1 � � (View in fixed font) >> >====== >> >> > � � � � � � Q1 >> > � � � � � �2n3906 >> >Vin >--+----. � �.-------+---+------+--> +13.3v >> > � � � | � � V �/ � � � �| � | � � �| >> > � � �R1 � �------ � � � | � R2 � �--- C1 >> > � � �470 � � | � � Q2 � | � 1k � �--- 15uF >> > � � � | � � �| � 2n3904 | � | � � �| >> > � � � '------+---. � � / � === � �=== >> > � � � � � � � � � \ � ^ >> > � � � � � � � � � ----- >> > � � � � � � � � � � | >> > � � � � � � � � � � R3 >> > � � � � � � � � � � 33 >> > � � � � � � � � � � | >> > � � � � � �+14v >---' >> >> >LT Spice says 31uV of the 50mV 1KHz ripple gets through (32dBv), >> >and the load step is 340uV. �That's a lot stiffer than the original, >> >which >> >had a 4.5mV load step (d(i) = 2mA for both). >> >> >The Sziklai version has the same ripple; I don't quite understand >> >how Early explains that--Early should wreck the load step response >> >too, shouldn't it? >> >> >FIG 1's load step is only 60uV if you replace R1 with a 5mA current >> >source, >> >the 1KHz ripple stays the same. >> >> >This shunt filter only needs 200mV headroom: >> >> >FIG. 2 >> >====== >> > � � � � � � � � � � � � � � � R1 >> >+15V >--+------------------/\/\/\--------+--> Vout = 14.8v >> > � � � �| � � � � � � � � � �5 � � � � � | >> > � � � �| � � � � � � � � � � � � � � � �| >> > � � � �| � � � � � � � � � � � � � � � �| >> > � � � �| � � � � � � � � � � � � � � � �| >> > � � � �| � � � �.-------+------+--------+ >> > � � � �| � � � �| � � � | � � �| � � � �| >> > � � � �| � � � �| � � � | � � R6 � � � �| >> > � � � �| � � � �| � � � | � � 1k � � � �| >> > � � � �| � � � R3 � � �R5 � � �| � � �|<' Q3 >> > � � � �| � � �2.7M � � 10K � � +------| � 2n3906 >> > � � � �| � � � �| � � � | � � �| � � �|\ >> > � � � �| � � � �| � � � | � �|/ Q2 � � �| >> > � � � �| � � � �| � � � +----| �2n3904 �| >> > � � � �| � � � �| � � � | � �|>. � � � �| >> > � � � �| � C1 � | � �|<' � � � | � � � �| >> > � � � �'---||---+----| �Q1 � � '--------+ >> > � � � � � 10uF � � � |\ 2n3906 � � � � �| >> > � � � � � � � � � � � �| � � � � � � � �R4 >> > � � � � � � � � � � � �| � � � � � � � 4.7R >> > � � � � � � � � � � � �| � � � � � � � �| >> > � � � � � � � � � � � === � � � � � � �=== >> >> >LT Spice says 20dBV rejection @ 1KHz, zero @ d.c., natch. >> >> Only 100 dB to go! > >That's 20dBV, e.g., (ripple in)/(ripple out) = 100. Pretty good for >standard parts with no trimming, I thought. Better cancellation needs >more accurate parts, e.g. op amp + precision resistors. I'm used to dBV meaning 20*log(volts), namely 100 volts is +40 dBV. It's an absolute level thing like dBm or dBuw. If a voltage regulator has 1 volt p-p ripple at its input and 10 mV at its output, its PSRR is 100:1 or 40 dB. > >Do you really need that ratio >= 10^12 ? Or do you mean dB(power), >i.e. (ripple in)/(ripple out) >= 10^6? I want any switcher noise (or any other noise!) to be below 1 nV in any 1 Hz bandwidth referred to my input. The box is the size of a small sandwich and is full of stuff. A microvolt of switcher noise on a critical power rail would probably make a visible birdie in somebody's data spectrum. Like having roaches in the salad. If my switcher has, say, 100 mV of ripple, 1e6:1 reduction, 120 dB, to 100 nV, might just do. 140 dB would be better. > >> But I don't understand Q1s biasing. > >Nope, you understand it fine! R2 got overlooked in the ASCII-art >conversion--5k from Q1(b) to GND. > >> But I can replace all that stuff after R1 with a big polymer aluminum >> cap and get about the same rolloff, probably better at high >> frequencies. > >If you've got the room that sounds fine. > > >> >I used transistors because they're fast--for canceling wideband noise. >> >> >You could use op-amps or TLV431 or such for accuracy and get make a >> >shunt regulator / noise canceler with much better 1KHz rejection, plus >> >load regulation. >> >> >Silliness, but fun. >> >> *I'm* not having much fun. I've got a circuit that needs nV/fA noise >> levels and it's beseiged from all directions. Johnson noise. Shot >> noise. Power supplies coupling in through diode junctions. Switchers >> inches away. And I'm supposed to Gerber it tomorrow. >> >> Wish you were here. > >It sounds like a lovely challenge, with a few shields tossed in the >mix. Not unlike RF receivers, methinks--those might inspire. Milled aluminum blocks this time. John
From: John Larkin on 24 May 2010 18:42 On 23 May 2010 16:54:54 -0700, Winfield Hill <Winfield_member(a)newsguy.com> wrote: >dagmargoodboat(a)yahoo.com wrote... >> >> This shunt filter only needs 200mV headroom: >> >> FIG. 2 >> R1 >>+15V >--+------------------/\/\/\--------+--> Vout 14.8v >> | 5 | >> | | >> | .-------+------+--------+ >> | | | | | >> | | | R6 | >> | | | 1k | >> | R3 R5 | |<' Q3 >> | 2.7M 10K +------| 2n3906 >> | | | | |\ >> | | | |/ Q2 | >> | | +----| 2n3904 | >> | | | |>. | >> | C1 | |<' | | >> '---||---+----| Q1 '--------+ >> 10uF |\ 2n3906 | >> | R4 >> | 4.7R >> | | >> ------+----------------+---- > > Nice ASCII art. Is fig 2 from your feverish brain? > > I see your idea, invert the ripple and subtract it out. > Good. To do that the cancellation amplifier needs to > be biased class A, so it can work over the entire ripple > range. It should continuously draw current from the > supply through R1, and superimpose the inverted ripple > signal on top of that. R4 can be trimmed to optimize. > The new R7 should be sized to handle the p-p ripple. > > Then John's delicate C-multiplier filter can follower, > with all the heavy lifting having been done. > > +15V >--+-----------------/\/\/\--------+--> Vout 14.8v > | 5 | > | | > | .------+------+--------+ > | | | | | > | | | R6 | > | | | 1k | > | R3 R5 | |<' Q3 > | 2.7M 10K +------| 2n4403 > | | | | |\ > | | | |/ Q2 | > | C1 | +----| 2n3904 | > '---||---+ | |>. | > 10uF | |<' | | > +----| Q1 '--------+ > | |\ 2n3906 | > R7 | R4 > TBD 27k | 4.7R > | | | > --+------+---------------+---- How about an opamp powered from Vout, with a resistor from the opamp output to ground? Let the opamp supply current fight the output ripple. That's thermally stable, simple, high gain, and tunable. (except I need regulation, too) John
From: Mike on 24 May 2010 18:50 Mike <spam(a)me.not> wrote: [...] > Is that spiceable? I made a simple circuit with a voltage source > driving the base and a cap on the emitter. I tried various transistors > such as 2N2222 and 2N2369, and various ESR and ESL values for the cap. I looked at this some more, and added a cap directly across the transistor from collector to emitter. The attenuation curve is like a bathtub. The capacitor in the emitter affects the low frequency. The C-E cap and ESL change the high frequency side. These are rational effects, and tend to say SPICE is telling the truth. But this says the ratio of the C-E cap and the emitter cap have no bearing on the attenuation, since they affect the opposite ends of the spectrum. One thing that had a dramatic affect on the attenuation is the emitter current. Going one order of magnitude up reduced the attenuation a great deal, and dropping the current to 1 mA finally gave close to -140dB. This says the low noise supply should be used only for the sensitive parts of a circuit, and as soon as the design permits, run the rest of the circuit on noisier supply voltages. It's not clear what the emitter current is changing, but there has to be a measurable parameter for the transistor that indicates how well it will perform in this application. But if this analysis holds water, it means I have learned something I didn't know before. Thanks, Mike
From: John Larkin on 24 May 2010 18:56 On Mon, 24 May 2010 14:35:59 -0400, Phil Hobbs <pcdhSpamMeSenseless(a)electrooptical.net> wrote: >On 5/24/2010 2:12 AM, John Larkin wrote: >> On Sun, 23 May 2010 21:45:06 -0700 (PDT), dagmargoodboat(a)yahoo.com >> wrote: >> >>> On May 23, 9:44 pm, Phil Hobbs >>> <pcdhSpamMeSensel...(a)electrooptical.net> wrote: >>>> Winfield Hill wrote: >>>>> dagmargoodb...(a)yahoo.com wrote... >>>>>> This shunt filter only needs 200mV headroom: >>>> >>>>>> FIG. 2 >>>>>> R1 >>>>>> +15V>--+------------------/\/\/\--------+--> Vout 14.8v >>>>>> | 5 | >>>>>> | | >>>>>> | .-------+------+--------+ >>>>>> | | | | | >>>>>> | | | R6 | >>>>>> | | | 1k | >>>>>> | R3 R5 | |<' Q3 >>>>>> | 2.7M 10K +------| 2n3906 >>>>>> | | | | |\ >>>>>> | | | |/ Q2 | >>>>>> | | +----| 2n3904 | >>>>>> | | | |>. | >>>>>> | C1 | |<' | | >>>>>> '---||---+----| Q1 '--------+ >>>>>> 10uF |\ 2n3906 | >>>>>> | R4 >>>>>> | 4.7R >>>>>> | | >>>>>> ------+----------------+---- >>>> >>>>> Nice ASCII art. Is fig 2 from your feverish brain? >>>> >>>>> I see your idea, invert the ripple and subtract it out. >>>>> Good. To do that the cancellation amplifier needs to >>>>> be biased class A, so it can work over the entire ripple >>>>> range. It should continuously draw current from the >>>>> supply through R1, and superimpose the inverted ripple >>>>> signal on top of that. R4 can be trimmed to optimize. >>>>> The new R7 should be sized to handle the p-p ripple. >>>> >>>>> Then John's delicate C-multiplier filter can follower, >>>>> with all the heavy lifting having been done. >>>> >>>>> +15V>--+-----------------/\/\/\--------+--> Vout 14.8v >>>>> | 5 | >>>>> | | >>>>> | .------+------+--------+ >>>>> | | | | | >>>>> | | | R6 | >>>>> | | | 1k | >>>>> | R3 R5 | |<' Q3 >>>>> | 2.7M 10K +------| 2n4403 >>>>> | | | | |\ >>>>> | | | |/ Q2 | >>>>> | C1 | +----| 2n3904 | >>>>> '---||---+ | |>. | >>>>> 10uF | |<' | | >>>>> +----| Q1 '--------+ >>>>> | |\ 2n3906 | >>>>> R7 | R4 >>>>> TBD 27k | 4.7R >>>>> | | | >>>>> --+------+---------------+---- >>>> >>>> The Kanner Kap uses an audio power amp to do this, applying a small >>>> amount of positive feedback to multiply the value of a BFC. Works OK, >>>> but it isn't worth paying royalties on. >>>> >>>> Cap multipliers are magic--especially two-pole ones. It's 0.7 volts >>>> well spent IMO. If Early is a worry, use a slower transistor--the >>>> ripple rejection is basically C_CE/C_BFC, with some degradation due to >>>> Early voltage and capacitor ESR. >>> >>> >>> Yep, two-pole--that's the stuff I was fiddling with whilst you guys >>> were posting...(ASCII takes time!) >>> >>> Fig. 3 >>> ====== >>> Q1 Q2 >>> 2n3904 2n3904 >>> +15V>--+--------. .----+---. .--+---> +13.3V >>> | \ ^ | \ ^ | >>> R1 ----- R3 ----- | >>> 100R | 100R | | >>> | R2 | | | --- C4 >>> +--/\/\/----+ +------' --- 100uF >>> | 100R | | | >>> C1 --- C2 --- --- C3 | >>> 100uF --- 100uF--- --- 100uF | >>> | | | | >>> === === === === >>> GND GND GND GND >>> >>> >>> Output ripple is LT-Spice undetectable. Zout ~= 2ohms. >>> >>> >>> Fig. 4 >>> ====== Q1 >>> 2n3904 >>> +15V>--+----------------+----. .----+-----> +13.3V >>> | | \ ^ | >>> R1 | ----- | >>> 3.3k | | --- C3 >>> | R2 |/ Q2 | --- 100uF >>> +--/\/\/---+---| 2n3904 | | >>> | 3.3K | |>. | | >>> | | | | === >>> C1 --- C2 --- +-------' GND >>> 10uF --- 10uF --- | >>> | | R3 >>> === === 10k >>> GND GND | >>> === >>> GND >>> >>> Buffer Q2 eliminates loading on filter R1C1-R2C2, greatly improving >>> transient response& recovery. >>> >>> The output at Q2(e) is super-clean, but changes in load current >>> modulate Re(Q1) and the drop across it, so output ripple is somewhat >>> worse than the reference. Zout is the same as Fig. 3. >>> >>> Early effect isn't as noticeable as Re, so far. >>> >>> I did a version following Fig. 4 with a one-pole C-mult stage, biased >>> off a divider from Q2(e), and a Sziklai PNP across the whole thing. >>> That means the single-pole stage operates as a cascode and sees no >>> d(Vce) to speak of. 1KHz ripple disappears, and Rout drops to about >>> 0.25 ohms. >>> >>> This version is silly with parts. There needs to be an op amp in >>> there somewhere to greatly simplify things, but it's time for me to >>> turn in. Hopefully these musings will inspire John to continue the >>> fight. >> >> >> This is what I have so far: >> >> ftp://jjlarkin.lmi.net/P14_reg.gif >> >> The wall wart is prefiltered by a C-L-C filter that should buy me >> about 40 dB at the switcher frequency. Then this thing should be good >> for maybe 100 more. Then I have some more RCs before the photodiodes >> and a couple of other critical things. >> >> This regulates to 13.4 to allow some headroom here and there. >> >> The LM8261 has about 10 nv/rthz noise, which is a whole nother story. >> >> John >> > >That's limited by the CMR of the op amp, though, which blows the whole >thing out of the water--no? That's the point of using the BJT in the >first place. CMRR and PSRR matter, certainly. But the transistor doesn't regulate, and doesn't seem to ripple reject super well at low frequencies, if the LT Spice 2N3904 model is to be believed. At high frequencies, ripple rejection of the transistor thing improves as the load cap and Re start making a lowpass. My 15 ohms is better than 2 ohms of Re, and drops less DC too. So the circuits really aren't all that different, but I'll have better low-frequency PSRR... clear down to DC. John
From: Phil Hobbs on 24 May 2010 21:04
On 5/24/2010 6:56 PM, John Larkin wrote: > On Mon, 24 May 2010 14:35:59 -0400, Phil Hobbs > <pcdhSpamMeSenseless(a)electrooptical.net> wrote: > >> On 5/24/2010 2:12 AM, John Larkin wrote: >>> On Sun, 23 May 2010 21:45:06 -0700 (PDT), dagmargoodboat(a)yahoo.com >>> wrote: >>> >>>> On May 23, 9:44 pm, Phil Hobbs >>>> <pcdhSpamMeSensel...(a)electrooptical.net> wrote: >>>>> Winfield Hill wrote: >>>>>> dagmargoodb...(a)yahoo.com wrote... >>>>>>> This shunt filter only needs 200mV headroom: >>>>> >>>>>>> FIG. 2 >>>>>>> R1 >>>>>>> +15V>--+------------------/\/\/\--------+--> Vout 14.8v >>>>>>> | 5 | >>>>>>> | | >>>>>>> | .-------+------+--------+ >>>>>>> | | | | | >>>>>>> | | | R6 | >>>>>>> | | | 1k | >>>>>>> | R3 R5 | |<' Q3 >>>>>>> | 2.7M 10K +------| 2n3906 >>>>>>> | | | | |\ >>>>>>> | | | |/ Q2 | >>>>>>> | | +----| 2n3904 | >>>>>>> | | | |>. | >>>>>>> | C1 | |<' | | >>>>>>> '---||---+----| Q1 '--------+ >>>>>>> 10uF |\ 2n3906 | >>>>>>> | R4 >>>>>>> | 4.7R >>>>>>> | | >>>>>>> ------+----------------+---- >>>>> >>>>>> Nice ASCII art. Is fig 2 from your feverish brain? >>>>> >>>>>> I see your idea, invert the ripple and subtract it out. >>>>>> Good. To do that the cancellation amplifier needs to >>>>>> be biased class A, so it can work over the entire ripple >>>>>> range. It should continuously draw current from the >>>>>> supply through R1, and superimpose the inverted ripple >>>>>> signal on top of that. R4 can be trimmed to optimize. >>>>>> The new R7 should be sized to handle the p-p ripple. >>>>> >>>>>> Then John's delicate C-multiplier filter can follower, >>>>>> with all the heavy lifting having been done. >>>>> >>>>>> +15V>--+-----------------/\/\/\--------+--> Vout 14.8v >>>>>> | 5 | >>>>>> | | >>>>>> | .------+------+--------+ >>>>>> | | | | | >>>>>> | | | R6 | >>>>>> | | | 1k | >>>>>> | R3 R5 | |<' Q3 >>>>>> | 2.7M 10K +------| 2n4403 >>>>>> | | | | |\ >>>>>> | | | |/ Q2 | >>>>>> | C1 | +----| 2n3904 | >>>>>> '---||---+ | |>. | >>>>>> 10uF | |<' | | >>>>>> +----| Q1 '--------+ >>>>>> | |\ 2n3906 | >>>>>> R7 | R4 >>>>>> TBD 27k | 4.7R >>>>>> | | | >>>>>> --+------+---------------+---- >>>>> >>>>> The Kanner Kap uses an audio power amp to do this, applying a small >>>>> amount of positive feedback to multiply the value of a BFC. Works OK, >>>>> but it isn't worth paying royalties on. >>>>> >>>>> Cap multipliers are magic--especially two-pole ones. It's 0.7 volts >>>>> well spent IMO. If Early is a worry, use a slower transistor--the >>>>> ripple rejection is basically C_CE/C_BFC, with some degradation due to >>>>> Early voltage and capacitor ESR. >>>> >>>> >>>> Yep, two-pole--that's the stuff I was fiddling with whilst you guys >>>> were posting...(ASCII takes time!) >>>> >>>> Fig. 3 >>>> ====== >>>> Q1 Q2 >>>> 2n3904 2n3904 >>>> +15V>--+--------. .----+---. .--+---> +13.3V >>>> | \ ^ | \ ^ | >>>> R1 ----- R3 ----- | >>>> 100R | 100R | | >>>> | R2 | | | --- C4 >>>> +--/\/\/----+ +------' --- 100uF >>>> | 100R | | | >>>> C1 --- C2 --- --- C3 | >>>> 100uF --- 100uF--- --- 100uF | >>>> | | | | >>>> === === === === >>>> GND GND GND GND >>>> >>>> >>>> Output ripple is LT-Spice undetectable. Zout ~= 2ohms. >>>> >>>> >>>> Fig. 4 >>>> ====== Q1 >>>> 2n3904 >>>> +15V>--+----------------+----. .----+-----> +13.3V >>>> | | \ ^ | >>>> R1 | ----- | >>>> 3.3k | | --- C3 >>>> | R2 |/ Q2 | --- 100uF >>>> +--/\/\/---+---| 2n3904 | | >>>> | 3.3K | |>. | | >>>> | | | | === >>>> C1 --- C2 --- +-------' GND >>>> 10uF --- 10uF --- | >>>> | | R3 >>>> === === 10k >>>> GND GND | >>>> === >>>> GND >>>> >>>> Buffer Q2 eliminates loading on filter R1C1-R2C2, greatly improving >>>> transient response& recovery. >>>> >>>> The output at Q2(e) is super-clean, but changes in load current >>>> modulate Re(Q1) and the drop across it, so output ripple is somewhat >>>> worse than the reference. Zout is the same as Fig. 3. >>>> >>>> Early effect isn't as noticeable as Re, so far. >>>> >>>> I did a version following Fig. 4 with a one-pole C-mult stage, biased >>>> off a divider from Q2(e), and a Sziklai PNP across the whole thing. >>>> That means the single-pole stage operates as a cascode and sees no >>>> d(Vce) to speak of. 1KHz ripple disappears, and Rout drops to about >>>> 0.25 ohms. >>>> >>>> This version is silly with parts. There needs to be an op amp in >>>> there somewhere to greatly simplify things, but it's time for me to >>>> turn in. Hopefully these musings will inspire John to continue the >>>> fight. >>> >>> >>> This is what I have so far: >>> >>> ftp://jjlarkin.lmi.net/P14_reg.gif >>> >>> The wall wart is prefiltered by a C-L-C filter that should buy me >>> about 40 dB at the switcher frequency. Then this thing should be good >>> for maybe 100 more. Then I have some more RCs before the photodiodes >>> and a couple of other critical things. >>> >>> This regulates to 13.4 to allow some headroom here and there. >>> >>> The LM8261 has about 10 nv/rthz noise, which is a whole nother story. >>> >>> John >>> >> >> That's limited by the CMR of the op amp, though, which blows the whole >> thing out of the water--no? That's the point of using the BJT in the >> first place. > > CMRR and PSRR matter, certainly. But the transistor doesn't regulate, > and doesn't seem to ripple reject super well at low frequencies, if > the LT Spice 2N3904 model is to be believed. At high frequencies, > ripple rejection of the transistor thing improves as the load cap and > Re start making a lowpass. My 15 ohms is better than 2 ohms of Re, and > drops less DC too. So the circuits really aren't all that different, > but I'll have better low-frequency PSRR... clear down to DC. > > John > > But for photodiodes, you don't care too much about the low frequency stuff, since it's in series with the photodiode capacitance. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal ElectroOptical Innovations 55 Orchard Rd Briarcliff Manor NY 10510 845-480-2058 hobbs at electrooptical dot net http://electrooptical.net |