BC41B143A-DS-002PD Datasheet, PDF (56/89 Pages) List of Unclassifed Manufacturers – BlueCore 4-ROM CSP EDR Single Chip Bluetooth v2.0 + EDR System

Device Terminal Descriptions
The frequency trim is described by Equation 11.5.
Δ(F_x ) _{= pullability × 55 ×10−3(ppm / LSB)}
F_x
Equation 11.5: Frequency Trim
Where F_x is the crystal frequency and pullability is a crystal parameter with units of ppm/pF. Total trim range is 63
times the value above.
If not specified, the pullability of a crystal can be calculated from its motional capacitance with Equation 11.6.
∂(F_x )
∂(C)
=
F_x
⋅
C_m
4(C_l + C₀
)²
Equation 11.6: Pullability
Where:
C₀ = Crystal self capacitance (shunt capacitance)
C_m = Crystal motional capacitance (series branch capacitance in crystal model). See Figure 11.6.
Note:
It is a Bluetooth requirement that the frequency is always within ±20ppm. The trim range should be sufficient
to pull the crystal within ±5ppm of the exact frequency. This leaves a margin of ±15ppm for frequency drift
with ageing and temperature. A crystal with an ageing and temperature drift specification of better than
±15ppm is required.
11.3.4 Transconductance Driver Model
The crystal and its load capacitors should be viewed as a transimpedance element, whereby a current applied to
one terminal generates a voltage at the other. The transconductance amplifier in BlueCore4-ROM CSP uses the
voltage at its input, XTAL_IN, to generate a current at its output, XTAL_OUT. Therefore, the circuit will oscillate if
the transconductance, transimpedance product is greater than unity. For sufficient oscillation amplitude, the
product should be greater than 3. The transconductance required for oscillation is defined by the following
relationship:
g_m
>
(2πF_x )²R_m((C₀
3(C_t1 +C_trim )(C_t2 + C_trim )
+ C_int )(C_t1 + C_t2 + 2C_trim ) + (C_t1 + C_trim )(C_t2
+ C_trim ))²
Equation 11.7: Transconductance Required for Oscillation
BlueCore4-ROM CSP guarantees a transconductance value of at least 2mA/V at maximum drive level.
Notes:
More drive strength is required for higher frequency crystals, higher loss crystals (larger Rm) or higher
capacitance loading.
Optimum drive level is attained when the level at XTAL_IN is approximately 1V pk-pk. The drive level is
determined by the crystal driver transconductance, by setting the PS Key KEY_XTAL_LVL (0x241).
11.3.5 Negative Resistance Model
An alternative representation of the crystal and its load capacitors is a frequency dependent resistive element.
The driver amplifier may be considered as a circuit that provides negative resistance. For oscillation, the value of
the negative resistance must be greater than that of the crystal circuit equivalent resistance. Although the
BlueCore4-ROM CSP crystal driver circuit is based on a transimpedance amplifier, an equivalent negative
resistance can be calculated for it with the following formula in Equation 11.8.
R_neg
>
g_m(2πF_x )²(C₀
3(C_t1 +C_trim )(C_t2 + C_trim )
+ C_int )((C_t1 + C_t2 + 2C_trim ) + (C_t1 + C_trim )(C_t2
+ C_trim ))²
Equation 11.8: Equivalent Negative Resistance
BC41B143A-ds-002Pd
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