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From: email@example.com (Michael Stein)
Subject: Re: Querry, Kick Starting Crystal Oscilator.
Date: Mon, 11 Nov 2002 06:00:16 +0000 (UTC)
Organization: University of California, Los Angeles
References: <3DCA905A.59FD928B@mmm.com.DELETETHIS> <3DCC9A71.7DF3C3A9@mfi.net>
NNTP-Posting-Date: Mon, 11 Nov 2002 06:00:16 +0000 (UTC)
User-Agent: slrn/0.9.7.1 (Linux)
Here's a simple 32 KHz oscillator circuit:
220K \ 1M \
+---> output |
32 KHz Xctl | |
from |x| 2n5089 C |
output | |x| | | Q1 E |
--- 33p --- 33p \ | | (bootstrap)
--- --- / +--------||---------+--> Vbias
| | 1M \ | .001 |
gnd gnd / | |
| \ \
| / /
Vbias \ 100K 470K \
This is derived from the low power circuit here:
with the bootstrap bias typo corrected (and I happened to use
a .001 uF instead of a .002 uF capacitor in the bootstrap circuit).
Also the 2n5089 isn't just any NPN. I don't know if it is required but
it's a low level (& low noise) so it has high beta at low currents (uAs).
>> Like most crystals, those have a Q of 60,000 to 90,000 which
>> means they'll take to 2 to 3 seconds to reach 50% of the full
>> oscillation energy. That's the way it goes; the energy cannot
>> simply be kick-started into the crystal.
Observation shows the delay, I can really see the oscillation build over
about 2 seconds on the scope (looking at waveform at emitter).
This is all built on one of those white proto-boards (no SPICE).
What's interesting is that disconnecting the feed from the "output" to
the crystal shows the oscillation fading down over about the same time.
It's possible to run it up and down manually, over a second each way.
And from loop closure to full amplitude is 5 to 6 seconds, the 2 seconds
was just when it became visible on the .5 V range. It appears that
during the last few seconds the amplitude triples about every second.
So this circuit has a startup delay, but can it be fixed?
Running the circuit open loop as a filter, I feed it a 5 V pp sq wave
from a 4046 buffered oscillator via 100K series and 470K to gnd to xctl
(instead of from "output"). I can see that the output amplitude of the
circuit varies (the crystal is a filter). Even small frequency changes
quickly cause large changes in amplitude, however there is no problem
seeing changes faster than one second.
So it's not the crystal causing the slow start. Perhaps it's
the circuit. Once running the the oscillator only needs unity gain.
The above ampifier has a gain of about 2 (220K/100K). Perhaps a bit
more gain will get the amplitude to build faster. I added the following
(it gets it's signal and bias from the emitter of Q1):
22K / to scope
| .01 10K | 100K
+----||--/\/\/\---+----+----/\/\----> to xctl input
| | |
from Q1 C -|- |
>------B /_\ \_/ 2x1n4148
emitter Q2 E 2n3904 | |
| gnd gnd
\ --- .1
3.3K / ---
gnd \ 500
This uses the original Q1 as an emitter follower (impedance conversion
and non-inverting). This stage inverts and adds more gain (up to 22K/500)
and also clips/limits the result. This also isn't low power anymore.
The start up is much faster (less than one second).
On the white proto-board there (must?) be some sort of feedback in
addition to the wire/intentional as opening the feedback loop now causes
the signal level to drop a bit and then stablize. This is with only the
side of the crystal connected to the base of Q1 connected (and only the
33 pF capacitor connected to the other crystal lead).
Shorting the open crystal lead to ground doesn't stop it. Grounding it
via a 22K resistor does send the amplitude down quite rapidly (but not
instantly) and the amplitude doesn't recover when disconnected from the
22K grounding resistor.
- - - - Some comments on the crystal - - - -
> The equivalent inductance associated with the motional impedance
> of a typical 32KHz crystal is HENRIES. How long would it take to
> get a significant current to flow through that amount of inductance?
> The series capacitance is picofarads. How much voltage would you have
> to apply to get significant current?
I don't know the specifications of my crystal, but it looks similar to
C-2 type and C type (32768 Hz) pdf specs:
Taking the specs for the C-TYPE/C-002RX (32768 Hz) at the bottom:
maximum drive level: 1 uW max
load cap: 6 pf
series resistance: 45 Kohm max
motional cap: 2.0 fF max
shunt cap: 0.8 pF max
insulation resistance: 500 Mohm min
That series capacitance is a lot less than picofards. The LC product
for 32Khz is:
1/(2*pi*32768)^2 = 2.3591e-11
With the motional capacitance of 2.0 fFk then L is:
2.3591e-11/2.0e-15 = 1.1796e+04
or 11796 H. Quite a bit larger than just "Henries".
So what's really happening? At full operation I'm seeing about 1.75 V
p-p at the emitter of Q1 so the voltage out of the crystal across the
33pf capacitor must be close to that. The model for the inside of the
crystal is supposed to look like this:
Where Lf is 11796 H, Cf is 2.0 fF, and C0 is .8 pf. Putting this in the
circuit context when the crystal isn't being feed from "output":
N/C >--+-----+--Lf----Cf--+---+--> to base & bias (amplifier input)
| | | |
| +-----C0-----+ |
--- 33p --- 33p
The current from the crystal into the 33 pF capacitor is (ignoring any
current going into the rest of the circuit):
Xc = 1/(2*pi*32768*33e-12) = 1.4718e+05
So I = V/Xc = (1.75 Vpp/2.8)/Xc = 4.2464e-06
or a bit over 4 uA. So what are the voltages inside the crystal *model*:
Vl = Xl*I = 2*pi*32768*11796*4.2464e-06 = 1.0313e+04
That's 10KV (and isn't really real?) But it would imply a peak energy
in the Cf capacitor (at 10 Kv) of:
1/2 CV**2 = (1/2)*(2.0e-15)*((10e3^2)) = 1.0000e-07
which is about .1 uW which seems reasonable (whatever is oscillating
inside the crystal has this energy stored).
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