# Frequency references: Crystal oscillator operation and specs

Other Parts Discussed in Post: CC2540

In part one of this series on frequency references I introduced crystal oscillators as a way of generating a very accurate reference clock.  Now let's say you have a radio (or two, since you want them to communicate), and are shopping for a crystal to use with it.  What do you need to know about the crystal specifications?

First, you need to choose a crystal that resonates at the correct frequency.  Your radio may support multiple reference frequencies, or it may require a specific value.  Common PLL reference clock frequencies are 10-50MHz.  (Also note that a 32 kHz crystal or some multiple of this may be required to generate a real time clock.  We’ll discuss this in more detail later.)  Let’s use the SimpleLink™ CC2540  for Bluetooth low energy solution as an example.

In the datasheet snapshot above, you can see it supports a 32MHz crystal with 6<ESR<60ohms and 10pF<CL<16pF.  What do these ESR and CL specifications mean?  Crystals can be modeled by a Butterworth Van *** (BVD) model, which is shown below.

The capacitor Co is the shunt capacitance caused by the crystal package.  Lm and Cm are the motional inductance and capacitance of the quartz crystal.  Rm is the motional resistance which models loss in the resonator.  The equivalent series resistance (ESR) is given by ESR=Rm(1+Co/CL)2.  The oscillator circuit in the SimpleLink CC2540 must create enough “negative resistance” to cancel out the loss from the ESR and sustain oscillation.  The load capacitance value CL is not a part of the BVD model but is specified for each crystal.  To get resonance at 32MHz, the crystal must be loaded with this capacitance CL.  If you use a crystal that has CL=10pF specified, but load it with CL = 5pF, you’ll get a higher frequency than you want - for example 32.0018MHz, which is 56ppm above 32MHz and when used as a reference to the PLL would violate the Bluetooth Low Energy specification.  Likewise, if you load the crystal with a CL value that is higher than what it is specified for, you’ll get a frequency lower than desired.  If CL is far too high, your crystal oscillator may not be able to cancel out loss from the crystal ESR and will not oscillate.   Many different crystals will meet the CC2540 requirements with various tradeoffs on size and performance.  The crystal selection guide here lists some of them.

In summary, in choosing a crystal, be sure to pick one with the correct center frequency and that has ESR and CL values supported by your radio.

Part three of my series, where I will continue to dive into this topic, is coming soon.  If you have questions in the meantime, feel free to comment below!

• Thanks for pointing that out, Ronald.  The link needed to be updated after a new version of SWRA372 was released.  It should work now.

• Thanks for the great educational posts, Danielle! Maybe it's my browser, but the link embedded in the above sentence, "The crystal selection guide here lists some of them.", was 404 for me.

• Ahmet, thanks for catching this.  Equation 1 in SWRA372B is drawn incorrectly and should be CL=(C'1 * C'2) / (C'1 + C'2).  We will get this fixed.

• Tank you Danielle. Is there any problem on equation 1 in SWRA372B?