Question 3.3: Integer-N Synthesizer Designed for Settling Time Design an i...
Integer-N Synthesizer Designed for Settling Time
Design an integer-N synthesizer to operate at 2.4 GHz to 2.4835 GHz and which must be able to settle from a frequency step in 225 μs (ignoring cycle slipping, which will be discussed in the next section). The channel spacing for the radio is 1 MHz. These are similar specifications to those of a Bluetooth radio. After the system is designed, determine how much the loop filter attenuates the reference signal.
For 1-MHz channels, the reference frequency is 1 MHz. Using a damping constant of 0.707, then the settling time is \omega _{n} t = 7 from Figure 3.19. Then, substituting t = 225 μs results in \omega _{n} = 7/225 μs = 31.11 krad/s, or 4.95 kHz. This results in a bandwidth of about 10 kHz from Figure 3.14. Now, loop gain K, divider values (N), and component limitations are required to determine the time constants. If the reference frequency is 1 MHz, then N is 2,400 to 2,483.
The VCO is required to cover a tuning range of 83.5 MHz, but there must be additional tuning range to allow for process variations. A tuning range of 10%, or about 250 MHz, seems necessary, as ±5% seems quite possible. Thus, a VCO constant of 250 MHz/V, or about 1.6 Grad/s/V, can be expected, assuming a 2-V supply and some room on either side of the rails. Now the remaining loop components that need to be determined are the charge pump current I, the integrating capacitor value C_{1} , and the phase-lead correction resistor R. From (3.22),
C_{1} =\frac{IK_{VCO} } {2\pi \cdot N\omega ^{2}_{n} } (3.22)
the ratio of C_{1} and I can be determined:
\frac{C_{1} } {I} =\frac{K_{VCO} } {2\pi \cdot N\omega ^{2}_{n} } =1.08\cdot 10^{-4}If C_{1} is chosen to be 5 nF, then the charge pump current is I = 46.3 mA. Note that this capacitor could not be integrated, but loop filters are often realized off chip. Now, making use of (3.23),
R=2\zeta \sqrt{\frac{2\pi \cdot N} {I K_{VCO} C_{1} } } =\zeta \frac{4\pi \cdot N\omega _{n} }{IK_{VCO} } (3.23)
the loop filter resistor R can be determined as well:
R=2\zeta \sqrt{\frac{2\pi \cdot N} {I K_{VCO} C_{1} } } =2\left(0.707 \right) \sqrt{\frac{2\pi \cdot 2,400} {46.3\mu A \cdot 1.6 \frac{Grad} {s} \cdot 5 nF } } 9.02 K \OmegaThe reference at 1 MHz is two decades higher than the loop corner frequency of 10 kHz. If we assume a first-order roll off for the loop of 20 dB/dec, then the reference signal will be attenuated 40 dB by the loop. Additional filtering may also be achieved by adding C_{2} = 500 pF.
