# Question: Component selection for a stable Local Oscillator

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#### Mr.Cool This post is long, so bare with me. I am attempting to design an FM receiver from scratch. My question, described below, is regarding practicle limits of quality factors. How do i chose components such that the local oscillator resonates at a specific frequency AND is stable..

Here is the calculation thought process, feel free to point out any errors i may have:

The Transmitter (Tx) sends the servo signals along a carrier frequency. In this case, the Tx carrier frequency is 75.590MHz. This is the frequency band (75MHz) allocated by the US FCC for mobile land based remote control , hobby, use. The Receiver (Rx) is based on the MC13111A “all in one” cordless phone chip. It will be designed to receive the Tx’s carrier frequency of 75.590 MHz. The antenna picks up this signal and transfers it to the first mixer, MIX1, where it is mixed with the first local oscillator, LO1. The output of MIX1 is determined by equation 1:

(1) FRF - FLO = FIF ;
***where FRF = Tx carrier frequency, given as 75.590MHz, FLO = LO1 frequency, to be calculated & FIF = intermediate frequency, chosen to fit a common filter value
***
Therefore: 75.590MHz - FLO = 10.7MHz
FLO = 64.89MHz

Now we know that the first local oscillator, LO1, must have a natural resonate frequency of 64.89MHz.

(2) Since: f = 1 / [2*p*(Lext*Cext)^½] ; ***where Lext = externally connected inductor, Cext = externally connected capacitor, and f = first local oscillator frequency
Pins 37 & 38 of the MC13111A chip is where we connect an LC circuit (Lext & Cext) to form the first local oscillator. According to page 24 of the MC13111A datasheet we first must choose a value for Lext, based on the information derived from figures 34&35.

The goal is to create a stable LO1. Stability is achieved by having the “Quality” factor of our LC circuit above that of the MC13111A (at pins 37&38). To calculate what the quality factor of our LC circuit is we use equation 3:

(2) Q = Rp / XL

***where Q = quality factor
Rp = internal parallel resistance (fig. 35 of datasheet)
XL = Reactance of the Lext @ LO1 frequency, (XL = 2p*f*Lext)

But we still need more information so that we can obtain useful information from figures 34&35. We know the frequency operation is @ LO1 = 64.89MHz. We can choose CAPACITOR SELECT (figure 35) to be #C10. Recall that this capacitance is programmed in via the microprocessor of the MC13111A. We pick #C10 because it is somewhere in the mid-range of the selectable capacitors, C10 = 10.5pF. This way, if we must fine tune the circuit later – we can have the option of raising or lowering this value by programming the CAPACITOR SELECT to give a higher or lower capacitance value as required. With this information we can extrapolate figure 35 to reveal the value of the internal parallel resistance, Rp = 10K.

Right… So now we have a partial solution of equation (2) above. Note that if we substitute in for XL we find that to solve equation (2) what we really need to know is the value for Lext. Now refer to figure 34 of the datasheet and find a graph that relates Lext Vs. Q factor (of the MC13111A). Putting these two observations together and we have essentially two equations and one unknowns. The first equation is Q factor of the LC circuit (found in equation (2) ). The second unknown is the Q factor of figure 34. The unknown that is common between both equations is Lext. Therefore, we can now determine Lext such that the resulting LC circuit is stable. For instance, selecting Lext = 300nH we find that the Q factor of Figure 34 is approximately 20 while the Q factor of equation (2) is calculated to be 81. Since equation (2) represents the quality factor of our LC circuit, and the rule as mentioned was that this Q factor had to be higher than the Q factor of the MC13111A, then we have achieved our goal.

My questions are: - What is the practical upper limit of the Q factor of equations (2) ? We are somewhere around 4 times greater, is this “ok” ?

@!@ wow... you made it to the end.. I applaud you for not falling asleep ;P

Mr.Cool

#### Pim

##### Member level 3 Do you have a URL where the datasheet you refer to could be downloaded for viewing and pondering?

The inductance value you mention (300 nH) is not that large. Do you have in mind to implement it on the circuitboard or make use of a ready-made discrete component?

Regarding the question of stability of an oscillator - if not locked in a PLL the stability of the frequency is determined by the circuit, component drifts, supply voltage, temperature etc. Another question re stability is that if a circuit is stable (generally speaking), it wont oscillate. You must have a minimum gain at a certain phase change from input to output of the oscillator for it to oscillate. Should the frequency-determining circuit (L/C/R) be such that the damping is too high, i.e. the Q-value of the circuit is too low, then you wont get enough gain through the oscillator loop with the result that the oscillator wont oscillate.

If I would have had the datasheet at hand I would be able to help you more, I hope.

#### BigBoss If your circuit is a parallel circuit , to increase the Q factor , decrease L value and
increase the C value to maintain the resonance frequency.
Another solution , in a a parallel resonance circuit there two resonance point. One of them comes from parasitic capacitance of the coil and self inductance of the coil and second one is the intrinsic resonance frequency.
Therefore, for increasing Q factor of a resonance circuit , decrease the parasitic capacitance of the interwounds of the coil. For to do this expand the coil if it's air core coil and use silver clad wire. Becasue
regarding to skin effect of the waves , currents flow outher conductor, so decrease the resistance of the coil by cladding silver. And increase the capacitance value to maintain the same result and use high quality "mica" or porcelene capacitors .

Formule: Q=(1/R)*SQTR( C/L ) for a parallel resonance circuit.

#### unkarc

##### Full Member level 5 Hi Mr.Cool,

There must be negative impedance between pins 37&38 because of the internal active oscillator stage. In case you try to "match" this impedance to that of the resonant parallel LC circuit, then you would gain a higher loaded Q which is the BIGGEST step towards oscillator stability.
How can you do this "matching"? If you try to use a tap on the Lext coil or use a link coupling coil of 1 or 2 turns (or a bit more turns), then you are there. In case of a tap (say at 1/4 or 1/3 of the total turns), one end of the parallel LextCext connects to pin 37 and the tap to pin 38 (or vica versa of course). In case of a link coupling, only the two ends of this coil connect to pin 37&38, the LextCext circuit remains unconnected, i.e. it is connected only by the magnetic coupling.
In this latter case you may have to use a small ferrite bead on one of the legs of the coupling coil to prevent the coupling coil oscillate somewhere with the parasitics!
However there are two (smaller) drawbacks:
1) In either case of the two couplings the tunning effect of the internal varicaps on the resonant frequency will be less.
2) You cannot choose much too loose coupling because the oscillator may not start oscillating! It would be the same case as if you apply a lower Q coil at Lext then the minimum neccessary from Fig. 34.

I fully agree with the reasonings of Pim and BigBoss. If you choose at least a minimum diameter of 0.6-0.7mm silver covered wire (CuAg) to wind your coil and observe a coil length/wire diameter ratio of around 0.45, then you have done the most possible to reach the minimum loss coil possible in a single layer air-core coil. In practical terms you can get with such a coil a Q of 300 or even greater at your frequency. Of course you have to consider the room available for that coil and it can be a limiting factor.

Your reasonings are correct all the way in your letter. The four times greater difference in Q is also ok: there is minimum required Q for the oscillator to start (this is in Fig 34) and from the other end, the higher Q could be allowed, the better. But this is limited from Fig. 35 and you get that limitation if you connect LextCext fully between pins 37&38. Here the cure is the tap or link coupling, together with using CuAg wire.

Regards, unkarc

PS to Pim: You can find data sheet of the MC13111 at h**p://e-www.motorola.com/brdata/PDFDB/docs/MC13110A.pdf

#### Mr.Cool thanks for the posts! very helpful, was exactly what i was looking for.

why do people ** out certain letters, like: h**P://e-www.motorola.com/brdata/PDFDB/docs/MC13110A.pdf

?

I have not had time to work further on your suggestions. I need to fully understand them first! When/if this remote control system if finished, i will publish the results here. (well, somewhere in elektroda.pl)

Enjoy
Mr.Cool

#### unkarc

##### Full Member level 5 Hi,

--------------------------------------------
"why do people ** out certain letters, like: h**P://e-www.motorola.com/brdata/PDFDB/docs/MC13110A.pdf ?"""
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Because it is included in the rules at elektroda forum boards (if the route links to outside of elektroda.pl).

Pleased we have been of help for you.

Regards, unkarc

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