Thread: Startup of crystal oscillator

Hi to all,
I'am working on crystal oscillator in classical Pirce configuration.
As an amplifier i use PMOS.
I want to ask if any of You know analytical relation between gm of the transistor and startup time of oscillator.
All books and articles say that startup time is dependent from Q of crystal and capacitances(or maybe i missed something). In my simulations i see that for higher biasing curent i have shorter startup time.
Wonder if any of You thought about that.

Best regards.
Marcin

" In my simulations i see that for higher biasing curent i have shorter startup time"
***
I dont think so.
In my memery, larger |neg-resistance| have shorter startup time. Higher biase current may not always cause larger |neg-resistance|, espacially for low frequency cystal oscillator.

Thanks for reply butterfish

To make things clear my oscillator is working on 27 MHz.
In the range that I checked startup time is getting shorter if gm increases.

Marcin

There is not direct relation between Gm-value and the start up time.
But the time will be shorter if you limit the output swing of OSC to a lower value.
But you know, when swing is lower, the phase noise will increase.

Beside, different structure has different startup time.

Dear Sir :
The start-up time is dependent on the crystal frequency , as like 4MHz is about 4ms , But you can add the start-up circuit for speeed the start-up time . It is hard to simulate , because we have add the initial condition for simulation. This is my experiment . As the crystal is ?KHx, like 78K or 32k. It is jard to simulation using transient simulation. Does anyone know how to start-up for this purpose , Thanks

Hi all and thanks for intrest in the topic.
To make clear what was my inital intrest i'am posting schamatic of my test bench and result graph. OSC is started with small pulse on vdd line.
You can see that for higher cutents oscilations grows faster.

jecyhale :
if ther is no relation betwen gm and start up time then what makes the diference ?

mitgrace:
simulation step neen to be set to very smal value - in my example crystal is 27MHz and step is fixed on 100ps. I'am not seting any initial conditions.

Start-up time depends on gm, especially on gm-opt, which is the optimum gm for a crystal oscillator to have the fastest start-up time.
Negative resistance -R(c) reaches max. when the gm reaches optimum.

The start-up time constant (r) depends inversely with R(c), so the larger R(c), the smaller time constant. That's why you see you increase gm, you decrease start-up time. Actually, there are another factors that controls your start-up as well. It is the DC biasing point where X1=X2 since when you starts up the circuit, it takes some time to reach X1=X2 and then both signals oscillates from small to large amplitude, so the large DC bias current, the faster X1=X2 and so it may also reduce the time to oscillate too.

You can simulate all the way from very small gm to very large gm to see the start-up time and you can find a peak for smallest start-up. Make sure you check it is gm, instead of biasing current. From this point, it is also meant that your design is not come to a optimum point where you still have margin to improve or trade-off between start-up time and power consumption.