Colpitts oscillator biasing

[init]

Hey guys, bit of a newbie question here. I'm looking at designing a colpitts oscillator using common emitter/source topology similar to this. I understand how to tune the tank circuit to create the desired resonance frequency but I am unsure how to go about biasing the circuit. From what I've read, the idea is to set the biasing conditions of the circuit such that "the oscillator works". What sort of biasing conditions does the circuit have to be set at to sustain oscillation?

[MrSlack]

This is basically a common emitter amplifier with a frequency dependent feedback network. So there are two bits to this. With respect to the amplifier, setting the base voltage (defining operating point) and setting the negative feedback to maintain stability. If I'm honest I've usually set this up empirically with some trimmers. Define the quiescent current at Ic/Ie (500uA is pretty good starting point), pick the emitter resistor to set the base voltage to about 1/2 vcc (Ve+0.6) then crank up the gain by changing the Rc/Re ratio so it oscillates but doesn't saturate the transistor. 99% success rate, not much mathematics which tends to be a little too ideal when it comes to building these in real life.

However this is a textbook circuit by the looks rather than a real one so I'd do some research on other designs first. They can be a lot simpler.

[init]

Thanks for the reply, I too have been fiddling with the biasing values in LTSpice until I get oscillation but I recognise this is a bit lazy and I would like some mathematical justification.

then crank up the gain by changing the Rc/Re ratio so it oscillates but doesn't saturate the transistor

I've heard from someone a lot better than me at this that the reason the oscillations occur is because the transistor saturates. Is this true?

[nugglix]

Hi!

I've heard from someone a lot better than me at this that the reason the oscillations occur is because the transistor saturates. Is this true?

No.
The oscillation starts way earlier.
If you inspect the start of the oscillation (via LTSpice) you will find that the signal amplitude
is rising in a exponential manner.
And this happens way before the transistor saturates.
So the saturation is clearly not the cause of the oscillation.

The oscillation purely depends on the positive feedback of the signal.
So you feed back a signal which is larger then the original, which in turn
gets amplified more and this is fed back...

Given the above it is clear that the transistor will reach the saturation region when
the signal becomes too large and no counter-measures are implemented.

The resulting signal will be heavily distorted when the transistor reaches saturation,
which results in a lot of harmonics.
I'm not sure if you want this to happen.

The oscillation is started from the inherent noise of the system which gets amplified,
frequency filtered and fed back into the amplifier.
If you simulate oscillators in LTSpice, it might help to activcate the startup option, so
that the power is ramped up like in the real world. This helps a lot in most cases.
The parts in LTSpice are very clean when it comes to noise.

Just my 2 mOhm

Cheers
  Guido

[MrSlack]

Agree with setting startup condition. Solves most oscillator starting conditions instantly! You can also inject some noise into LTspice easily with the random() function. Occasionally I introduce some 2-3mV noise into the supply - helps to isolate where I'm going to see noise floor being pushed up.

Also a practical tip: Make sure every stage in any RF/oscillator circuits you build is decoupled from all the others cleanly. You'll be surprised where unintended oscillators appear with dire consequences. You can do this at a basic level with a small resistor in series with the stage and a decoupling capacitor across the stage if you're a cheap ass like myself but something with better rejection like a small DC inductor would be a better idea.

[init]

Thanks for the tips guys 

I've given a go at simulating a basic topology

using arbitrary biasing values (whatever worked) and from my calculations w = sqrt(2/(LC)), the oscillation frequency should be ~100MHz using 51pF and 100nH. When I simulate the circuit, as evident from the image, the oscillation is at 9.4MHz. Are the parasitics of the FET model interfering with the oscillation frequency? The bypass caps are high passing with a low cutoff (from large input resistance) so they shouldn't interfere.

[MrSlack]

I wouldn't use a MOSFET. The gate capacitance is huge which kills them for this sort of application. Try a JFET (J113) or BJT first.

[nugglix]

Are the parasitics of the FET model interfering with the oscillation frequency?

Yes, they are part of the tank circuit.

See coments on attached circuit.

Btw, there are a lot of circuits on the internets, some even with descriptions.
Also some videos, like:
https://www.youtube.com/playlist?list=PL-I4mA2w8q4ZLWcUGmS6XCqmAdoNnGkyv

Hope thats helps.

Cheers
  Guido

[MrSlack]

Another VFO design as well, varactor tuned as an example. Peaked on 40m. I love how they all end up similar. mine is hitting a diode ring mixer though rather than an SA602 as I don't have any of them

Ignore the output filter though on mine - it doesn't work. Yet. 

[nugglix]

Nice!

One question though:
Why the low value of R6?
I fear this is a very heavy load on the tank.
Is this desired in this case?

As far as I can figure out the implications, it will lead
to more jitter (phase noise?).
Due to the reduced Q (bandwith) of the tank circuit.

[MrSlack]

It will indeed load it. The breadboard version has a 100k in there an RF choke, op amp buffer and 10 turn pot driving it. I was experimenting with how this affects the oscillator as I'd not used varactor diodes before. Must have left it in. TBH I'd got bored of LTspice by that stage and was soldering

I haven't worked out how to (cheaply) measure phase noise yet as I don't have an SA. On the todo list!

[nugglix]

Indeed amazing how things go into the same direction.   
I just designed a opamp driver for my varactor tuned oscillator.

Because I don't have a 10-turn pot, I used a summing-amplifier and
2 normal pots.
The values are hand-crafted to match the most (frequency) linear region
of my varactors.
The "real thing" will make use of a MCP607 though, but I don't have spice model
for it. So I used the TLC272 model.

I fear I'm running out of excuses to not start soldering the things together. 

[MrSlack]

Nice solution. Would have never have thought of that. Course + fine tuning is cheaper than a 10 turn as well. My 10 turn was stolen out of my parts mule scope's delay timebase - never would have bought one new. A decent Bourns one is £17! Only using varactors as they are smaller, lighter, cheaper and ubiquitous compared to air variable caps

I have found that the BB145's aren't very linear at all so far. Still playing with this idea. It's this or an AD9850 solution and a virtual dial which feels like cheating

Still need a decent jellybean rail to rail low voltage opamp for this sort of thing. I'm using a TL072 and two supplies at the moment which isn't ideal.

[orolo]

Colpitts is, at its heart, a Van der Pol oscillator: for small oscillations, it behaves as a forced oscillator. The condition to start oscillation is that the transconductance of the amplifier is greater than the product of series resistance, the two tank capacitances, and the square of the angular velocity; it is explained in the wikipedia article quite nicely. Since transconductance in a BJT is determined by collector current, that determines your bias point.

$$ g_m > R_s\cdot C_1\cdot C_2 \cdot \omega^2$$  where $$ g_m = \frac{I_C}{26e-3} $$

When the oscillator reaches steady state, the dynamics is totally different: you have reached the limit cycle in the oscillator. The BJT will be off most of the cycle, and only briefly conduct at the top of the cycle, saturating. In the common collector Colpitts, which I use most, the conduction cycle is about 25% of the total cycle, IIRC. A mechanic analogue is a Foucault pendulum in a science museum: the pendulum oscillates freely, and only gets a little push (via electromagnet) at one extreme of the oscillation.

Edit: formula and link.

[nugglix]

Nice solution. Would have never have thought of that. Course + fine tuning is cheaper than a 10 turn as well. My 10 turn was stolen out of my parts mule scope's delay timebase - never would have bought one new. A decent Bourns one is £17! Only using varactors as they are smaller, lighter, cheaper and ubiquitous compared to air variable caps

The idea is -- of course -- stolen. 

And yes, given the prices charged for variable caps and other "hobby" stuff, a bag of potis
from china is the cheapest solution.

I have found that the BB145's aren't very linear at all so far. Still playing with this idea. It's this or an AD9850 solution and a virtual dial which feels like cheating

The capacity shouldn't be linear over voltage, it should follow a square function. This
will make the frequency change linear over the control voltage.
Which I think is the desired behaviour - at least for my VFO.

Still need a decent jellybean rail to rail low voltage opamp for this sort of thing. I'm using a TL072 and two supplies at the moment which isn't ideal.

Ahhh in the search of the holy grail of opamp usage. 

I have some MCP607, MCP602 and MCP6021 and will try them, given I've the time.
Given that the MCP607 is available from aliexpress for $2.66 per 10 pcs and the MCP602
for $3.89/10pcs -- shipping included of course -- this seems to be the route to go.

[MrSlack]

The capacity shouldn't be linear over voltage, it should follow a square function. This
will make the frequency change linear over the control voltage.
Which I think is the desired behaviour - at least for my VFO.

To confirm, this is linear with respect to the output frequency vs tuning voltage. Not the capacitance vs tuning voltage. If you plot the varactor's capacitance versus voltage on lin-log it's still curved slightly which gives a compressed region in the pot travel. It might actually be a better outcome with a fine/course tuning pot system yet

Opamp holy grail. One day we will reach this

[nugglix]

To confirm, this is linear with respect to the output frequency vs tuning voltage. Not the capacitance vs tuning voltage. If you plot the varactor's capacitance versus voltage on lin-log it's still curved slightly which gives a compressed region in the pot travel. It might actually be a better outcome with a fine/course tuning pot system yet

Sorry, I thought you meant the capacity.

And this behaviour is the reason for the hand-tuned control voltage of my circuit.
I deliberately only use a portion of the possible tuning voltage and hope I found the
right range.

Now I need to wind the inductor. Didn't think of ordering some... 

And sorry for hijacking this thread.

[MrSlack]

I might try that way of providing linearity - it's a good idea.

My design approach is to see what inductor cores I have floating around first. Fortunately I had two micrometals T50-6's with known Al then stick some kynar around them based on http://toroids.info/ . Then work out the rest based on what NP0 ceramics I have around and what trimmers I can steal out of the junk I have lying around. There is no science here

Apologies too.

[uncle_bob]

Hi

Quick cookbook:

1) You need to bias the active device so it does not drift all over the place. That generally puts a volt or three on the emitter / source resistor.
2) You want enough current to give you transductance to provide 3 to 9 db of excess loop gain at turn on.
3) You want to bias the device so it clips (limits) in a "current cutoff" rather than a "voltage saturation" mode.

Do all that and it will work well, live long, pour your beer, and all sorts of wonderful stuff.

Bob