User Manual

Jennic
JennicJennic
Jennic
72 JN-DS-JN5139 v1.5 © Jennic 2008
B.1.2 Crystal Load Capacitance
The crystal load capacitance is the total capacitance seen at the crystal pins, from all sources. As the load
capacitance (CL) affects the oscillation frequency by a process known as ‘pulling’, crystal manufacturers specify the
frequency for a given load capacitance only. A typical pulling coefficient is 15ppm/pF, to put this into context the
maximum frequency error in the IEEE802.15.4 specification is +/-40ppm for the transmitted signal. Therefore, it is
important for resonance at 16MHz exactly, that the specified load capacitance is provided.
The load capacitance can be calculated using:
CL =
21
21
TT
TT
C
C
CC
+
×
Total capacitance inPT CCCC 1111
+
+
=
Where 1 C is the capacitor component
P C 1 is the PCB parasitic capacitance. With the recommended layout this is about 1.6pF
in C 1 is the on-chip parasitic capacitance and is about 1.4pF typically.
Similarly for 2T C
Hence for a 9pF load capacitance, and a tight layout the external capacitors should be 15pF
B.1.3 Crystal ESR and Required Transconductance
The resistor in the crystal equivalent circuit represents the energy lost. To maintain oscillation, power must be
supplied by the amplifier, but how much? Firstly, the Pi connected capacitors C
1
and C
2
with C
S
from the crystal,
apply an impedance transformation to Rm, when viewed from the amplifier. This new value is given by:
2
ˆ








+
=
L
LS
mm
C
CC
RR
The amplifier is a transconductance amplifier, which takes a voltage and produces an output current. The amplifier
together with the capacitors C1 and C2, form a circuit, which provides a negative resistance, when viewed from the
crystal. The value of which is given by:
2
21 ω ××
=
TT
m
NEG
C
C
g
R
Where m
g
is the transconductance
ω
is the frequency in rad/s
Derivations of these formulas can be easily found in textbooks.
In order to give quick and reliable oscillator start-up, a common rule of thumb is to set the amplifier negative
resistance to be a minimum of 4 times the effective crystal resistance. This gives
2
21 ω ×× TT
m
C
C
g
≥
2
4








+
L
LS
m
C
CC
R