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Design >> Mixed-Signal Design >> Negative resistance concept in Crystal oscillators
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Message started by hchanda on Feb 13^th, 2009, 3:16pm

Title: Negative resistance concept in Crystal oscillators
Post by hchanda on Feb 13^th, 2009, 3:16pm

Hi,

I read lot of papers deriving the negative resistance of the pierce amplifier based crystal oscillator design. I would like to understand intutively how a common source amplifier with C1 and C2 (which constitutes the cload of XO) would result in negative resistance?

Negative resistance implies that: If the voltage across the terminal is increasing then the current through this is decreasing.

So in the case of pierce amplifier based XO, let say if gate voltage is increased, then the drain current of the transistor increases which reduces the current through capacitor that is connected to drain. (Assuming a current source connected to drain) Since the current through capacitor is decreased is this considered as negative resistance? If this is the explanation then why does the negative resistance decrease when shunt capacitance of XTAL is taken into consideration? I would like to understand this concepts intutively not based on mathematical equations.

Title: Re: Negative resistance concept in Crystal oscillators
Post by pancho_hideboo on Feb 13^th, 2009, 9:05pm

Why is this post "Mixed-Signal Design" issue ? Is there any "Mixed-Signal" ?

hchanda wrote on Feb 13^th, 2009, 3:16pm:

I would like to understand this concepts intutively not based on mathematical equations.

I don't know a topology of your negative impedance generator.

Assume an ideal current drive(Iin=1A) of a simple negative impedance generator consisted from C1, C2 and Transistor.
And current of C2 is sum of current of C1 and current from Transistor.
Here former current is equal to Iin, latter current is gm*Voltage_C1 which is 90degree different from Iin.

So there could be negative real part in total sum voltage of C1 and C2.
This can be understood if you draw vector(phasor) diagram of Iin, Vc1, Vc2 and Vc1+Vc2.

Title: Re: Negative resistance concept in Crystal oscillators
Post by buddypoor on Feb 13^th, 2009, 11:35pm

hchanda wrote on Feb 13^th, 2009, 3:16pm:

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Negative resistance implies that: If the voltage across the terminal is increasing then the current through this is decreasing.

I am afraid that your understanding of a negative resistance is not correct. Look at the definition: Rneg=-V/I resp. I=-V/R.
This simply means that the current flows in the opposite direction but its value is identical to the pos. resistor case. A neg. resistor is something like a voltage controlled current source (as a pos. resistor is a voltage controlled current sink) .

Title: Re: Negative resistance concept in Crystal oscillators
Post by raja.cedt on Mar 21^st, 2009, 3:11am

hi,
i think for your question simple answer is first derive the common source amplifier input impedance with capacitive load,see there is -ve resistance as well as capacitance.If u can understand this clearly,then crystal oscillator is also similar

thanks,
Rajasekhar