SP8858 Просмотр технического описания (PDF) - Zarlink Semiconductor Inc

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SP8858

1·5GHz Professional Synthesiser

Zarlink Semiconductor Inc 

The selection of C1 and R1 is often approached by using

the standard representation for the second order characteristic

equation: s212zvn1vn2 and selecting the natural-loop

frequency and the damping factor z to give the desired

response. The time constants are calculated using:

2zvn = t1K/C1 and vn2 = K/C1 so that

C1 = K/vn2 and R1 = 2zvn/K

Alternatively, the loop filter and formula shown in Fig. 10b

can be used to introduce a pole in F(s) at 21/t2 which will

provide additional roll-off in the closed loop transfer

characteristic in order to attenuate the reference sidebands.

The closed loop transfer function becomes:

fo(s)

=

[s(t11t2)11]KVCOKPD

fi(s) [C1t2s31C1s21K(t11t2)s1K]

Care must be taken when choosing C2 to ensure that the

additional pole does not unduly affect the stability margins of

the loop. In practice, a simple and useful rule of thumb is to set

the desired second order response as above and then set C2

to be 1/10 of C1. It is advisable when designing third order or

SP8858

higher order loops to use CAD tools to assess stability.

Popular analysis tools taken from control theory, such as root

locus and Bode diagrams, are useful to aid the design of the

closed loop PLL system. AN194 describes these tools in more

detail and introduces a loop filter design methodolgy aimed at

optimising the phase noise performance.

Loop filter design example

Use the demonstration board to generate a 1GHz signal

with a resolution of 500kHz (N = 5000) and reference oscillator

frequency of 40MHz. Set natural loop frequency, vn, to

2p3104 rad/s and damping factor to 0·7. The MQE001-1016

VCO gain, KVCO, is nominally 25MHz/V. Set the phase detector

output current to 2mA so that KPD = 231023/2p A/rad.

Using the above formula, calculate the loop filter R and Cs.

K = 2p32531063231023/2p35000 = 10

C1 = 10/(2p3104)32 ≈ 2·531029

R1 = 230·732p3104/10 ≈ 8796

C2 = C1/10 ≈ 0·2531029

Realise the loop filter with C1 = 2·2nF, C2 = 220pF and

R1 = 8·2kΩ. The single sideband phase noise specturm for

this example is shown in Fig. 11.

C1

R1

Ii(s)

−

+

Vo (s)

Vo (s) / Ii(s) = [s(t111]/sC1

where t1 = C1R1

Fig. 10a

C2

C1

R1

Ii(s)

−

+

Vo (s)

Vo (s) / Ii(s) = [s(t11t2)11]/sC1(st211)

where t1 = C1R1 and t2 = C2R1

Fig. 10b

Fig. 10 Loop filters

0

210

220

230

240

250

260

270

280

290

2100

2110

2120

2130

2140

2150

2160

2170

10Hz

100Hz

1kHz

FREQUENCY

Fig. 11

10kHz

100kHz

11

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