#### Mr.Cool

##### Advanced Member level 2

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