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# Two port input impedance measurement

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#### rajath

##### Member level 2
input impedance measurement

Hi,

I'm designing a crystal oscillator using a parallel resonant circuit. I would like to measure the negative impedance of the active circuitry in the frequency range of interest. Since we need to to measure this across the resonator (with the resonator removed), can someone please suggest a way to do this in the Cadence environment?

I also had a basic question: Is the term "excess gain" same as "negative impedance"?

thanks,
rajath

#### xxargs

##### Full Member level 4
complex impedance measurement mcu

rajath said:
Hi,

I'm designing a crystal oscillator using a parallel resonant circuit.

I think you mean Piece-oscillator - very common used oscillator in MCU and digital world depend of easy implement with only a inverter.

Piece-oscillator using crystal as heavy inductance with outside capacitance in PI-network (inductance exist only between crystal serie resonanse and crystals parallell resonanse-point - and with outside PI-network capacitance, frequency place some point in middle between crystals internal resonance-point).

drawback is this solution is not high frequency stability depend of outside capacitance can adjusting frequency ten to couple of hundred Hz depend of value.

I would like to measure the negative impedance of the active circuit in the frequency range of interest. Since we need to to measure this across the resonator (with the resonator removed), can someone please suggest a way to do this in the Cadence environment?

I also had a basic question: Is the term "excess gain" same as "negative impedance"?

thanks,
rajath

I think is not a simple relation as above, but I know 'gain' can show as negative impedance outside unit circle in SmithChart. Look at wikipedia and google with 'negativer resistance' and 'negative impedance' - it's bit complicate and much to read...

If drivers not working in pure linear mode, in not easy to talk (or measure) negative impedance in single complex value for selected frequency. Impedance is depend of voltage and current levels on drivers in and output-port. For example 74HC04 have very difference gain and impedance if levels is saturated high (low gain, low impedance ), in more linear middle region (high gain, higher impedance) and hard driven to low level (low gain, low impedance).

If you simulate with model of crystal in some kind of SPICE enviroment - remember, in timedomain - start up time to stable level for oscillator can be very long depend of crystals very high Q-value, starting can also seems very fuzzy and different frequency to time crystal have energy stored enough to going be dominant in current and voltage flow and take over frequency decision in network - we talk part of seconds or more, simulate in ns resolution for example of 16 MHz crystal.

In same case - check how much power dissipated inside crystal model[1] after level stabilize (possible on of worlds most forgotten design parameters in MCU oscillator design ...) many modern low profile HC49/4H package crystal allow only 500 µW power loss inside crystal compare to old full size crystals handle 5 mW - read crystal spec carefully, and also how much total extern parallell capacitance crystal needs to make stamped frequency in piece-oscillator network (ie parallell-resonate design) . I see old design papers saying 10 pF, and newer papers saying 20 pF or 32 pF as 'standard' for make 'stamped ' frequency - you must know this in your design if you wanted more exact frequency.

For example - oscillator build around 74HC04-inverter need least 600 Ohm serial resistans on output to guarante not to overdrive modern (500µW) 16 MHz crystal, and watch clock crystal 32768 Hz needs serial resistance around 220kOhm - 1 MOhm to not be overdriven - and also save power on inverter depend of allow full swing square wave output from driver and spend only small time in middle voltage, power hungry, linear region in CMOS-oscillators solution. If you want (32768 Hz) oscillator going only on few µA, you must build this around transistors - not CMOS-circurits. (see google on pierce-ocillator)

Without serial resistor on 74HC04:s output - same crystal dissipate around 6-7 mW heat and can slowly wears out, possible shows as shifting frequency in step or after power off/on cycle depend of new spur-frequency going dominant, or simple broken after x thousand hours, depend of high mechanical stress (to high amplitude extesional or thickness shear vibration) on quarts disc inside crystal.

- remember 'mecahnical voltage' in crystal can be around 60000 t-t Volt with 1 volt feeding outside for 500 µWatt loss, and overdriven with 5 mW can make 'mechanical voltage' around 200000 Volt t-t for Q=100k crystal in pierce-network

[1]

You have know ESR (typical 80 Ohm for 16 MHz crystal), parallell C ( typical 7pF) , and Q-value ( typical 100000) in most crystal manufactorys data sheet, and from then can calculate ekvivalent Ls (in part of henry range) and Cs ( in femtofarad range) with:

Ls = R*Q/(2*PI*f)
Cs = 1/((((2*PI*f)^2)*R*Q) / (2*PI*f))

f is crystal serie resonance frequency.

### rajath

Points: 2

#### rajath

##### Member level 2
port input impedance

thanks a lot xxargs! Yeah transient simulation will take up quite a bit of time, and that's the reason I'm trying to get further insights into the circuit by AC analysis. It may not be accurate due to the non-linear nature during large amplitudes, but a good starting point anyway.
I have come across this statement that a resonant circuit with a large Q will take a lot of time to stabilize during transient simulation, but haven't been able to clearly figure out why! Any insights on that?

thanks,
rajath

#### xxargs

##### Full Member level 4
mcu impedance crystal oscillator

rajath said:
thanks a lot xxargs! Yeah transient simulation will take up quite a bit of time, and that's the reason I'm trying to get further insights into the circuit by AC analysis. It may not be accurate due to the non-linear nature during large amplitudes, but a good starting point anyway.
I have come across this statement that a resonant circuit with a large Q will take a lot of time to stabilize during transient simulation, but haven't been able to clearly figure out why! Any insights on that?

thanks,
rajath

High Q-value itself says crystal storing very much energy in resonant circurity inside and very little commumicate to outside world and make small bandwidh - good communicate to enviroment give high loss depend of outside load and make low Q-value - and wideband.

low-Q resonant cicurit starting fast and stopping fast - and sensitive on enviroments impedanse, interference on voltage and loss for result frequency. For example PLL with simple oscillator have low-Q resonance and make signal with much phase-noise.

High -Q resonant circurit starting slow and stopping slow - and very low sensitive for enviromental noise and crystal oscillator have in most case very low phase noise.

for example pierce oscillator allow small range frequency between crystals serial resonance point and crystals parallell seriell resonate point and open for enviromental sensivity (varying PI-coupled capacitance) and working with lower Q-value and more phase noise compare if oscillator working in crystal serial mode...

---

One metod to make faster, steady state driving in simulation is 'charge' serial capacitanse (or make current inside inductance) inside crystal model before starting simulation to say 60000 - 100000 Volt, and in simulation see if amplitude over serial inductor and serial condensator in crystal model still rising or going lower voltage - adjust voltage again to you make stable level - and you possible find point of steady working point of oscillator.

But this shortcut way cannot guartee if oscillator starting properly or not - oscillator possible to find other oscillate mode in start up ramp from DC-start transient or possible not will starting in wanted frequency.

For example can leaking resistance in MOhm-range resistance parallell over crystal (to quarantee starting CMOS-oscillator) make own RC-oscillator with PI-network without crystal influence and make unstable oscillation near crystall frequecy, but odd enough in frequency to not feeding energy enough compare to loss inside crystall to starting up properly.

Simulator can also going wrong way and only hopping between couple of state again and again and not willing to start to fully action in infinite time depend of simulate model missing termic noise and use limited resolution floating numbers - you can find not starting modes in simulator in case not happend i real world - take care on this and check on real thing - best models of componet/systems delevery only from physic reallity itself.

#### rajath

##### Member level 2
leaking resistance measure

thanks again!

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