Phase-Locked Loops In a phase-locked loop, the error signal from the phase comparator

is proportional to the relative phase of the input and feedback

signals. The average output of the phase detector will be constant
for High-Frequency when the input and feedback signals are the same frequency. The
usual equations for a negative-feedback system apply.

Receivers and Forward Gain = G(s), [s = jω = j2πf]

Loop Gain = G(s) × H(s)

Transmitters–Part 1 Closed−Loop Gain =

G(s)
1 + G(s)H(s)
by Mark Curtin and Paul O’Brien
This 3-part series of articles is intended to give a comprehensive Because of the integration in the loop, at low frequencies the steady
overview of the use of PLLs (phase-locked loops) in both wired state gain, G(s), is high and
and wireless communication systems. 1
In this first part, the emphasis is on the introductory concepts of VO /VI, Closed-Loop Gain =
H
PLLs. The basic PLL architecture and principle of operation is
described. We will also give an example of where PLLs are used in The components of a PLL that contribute to the loop gain include:
communication systems. We will finish the first installment by 1. The phase detector (PD) and charge pump (CP).
showing a practical PLL circuit using the ADF4111 Frequency 2. The loop filter, with a transfer function of Z(s)
Synthesizer and the VCO190-902T Voltage-Controlled
Oscillator. 3. The voltage-controlled oscillator (VCO), with a sensitivity of
KV /s
In the second part, we will examine in detail the critical
specifications associated with PLLs: phase noise, reference spurs 4. The feedback divider, 1/N
and output leakage current. What causes these and how can they Error Detector Loop Filter VCO
be minimized? What effect do they have on system performance? CP
+ e(s)
Kd Kv FO
FREF PD Z(s)
The final installment will contain a detailed description of the ( UREF ) - s ( UO )
blocks that go to make up a PLL synthesizer and the architecture
of an Analog Devices synthesizer. There will also be a summary of
synthesizers and VCOs currently available on the market, with a 1
list of ADI’s current offerings. N
Feedback Divider
PLL BASICS
Figure 2. Basic phase-locked-loop model.
A phase-locked loop is a feedback system combining a voltage-
controlled oscillator and a phase comparator so connected that If a linear element like a four-quadrant multiplier is used as the
the oscillator maintains a constant phase angle relative to a phase detector, and the loop filter and VCO are also analog
reference signal. Phase-locked loops can be used, for example, to elements, this is called an analog, or linear PLL (LPLL).
generate stable output frequency signals from a fixed low-frequency If a digital phase detector (EXOR gate or J-K flip flop) is used,
signal. The first phase-locked loops were implemented in the early and everything else stays the same, the system is called a digital
1930s by a French engineer, de Bellescize. However, they only PLL (DPLL).
found broad acceptance in the marketplace when integrated PLLs
If the PLL is built exclusively from digital blocks, without any
became available as relatively low-cost components in the mid-
passive components or linear elements, it becomes an all-digital
1960s.
PLL (ADPLL).
The phase locked loop can be analyzed in general as a negative-
Finally, with information in digital form, and the availability of
feedback system with a forward gain term and a feedback term.
sufficiently fast processing, it is also possible to develop PLLs in
A simple block diagram of a voltage-based negative-feedback the software domain. The PLL function is performed by software
system is shown in Figure 1. and runs on a DSP. This is called a software PLL (SPLL).

e(s) Referring to Figure 2, a system for using a PLL to generate higher

+ VO
Vi G(s) frequencies than the input, the VCO oscillates at an angular
– frequency of ωO. A portion of this signal is fed back to the error
detector, via a frequency divider with a ratio 1/N. This divided-
down frequency is fed to one input of the error detector. The other
input in this example is a fixed reference signal. The error detector
H(s) compares the signals at both inputs. When the two signal inputs
are equal in frequency, the error will be constant and the loop is
Figure 1. Standard negative-feedback control system model. said to be in a “locked” condition. If we simply look at the error
signal, the following equations may be developed.

Analog Dialogue 33-3 (© 1999 Analog Devices) 1

 When GH is much greater than 1, we can say that the closed loop
ΦO
()
e s = Φ REF −
N
transfer function for the PLL system is N and so
FOUT = N × FREF
de s ()=F REF −
FO The loop filter is a low-pass type, typically with one pole and one
dt N zero. The transient response of the loop depends on:
When 1. the magnitude of the pole/zero,

() FO 2. the charge pump magnitude,

e s = constant , = FREF
N 3. the VCO sensitivity,
Thus 4. the feedback factor, N.
FO = N FREF All of the above must be taken into account when designing the
In commercial PLLs, the phase detector and charge pump together loop filter. In addition, the filter must be designed to be stable
form the error detector block.When FO ≠ N FREF, the error detector (usually a phase margin of π/4 is recommended). The 3-dB cutoff
will output source/sink current pulses to the low-pass loop filter. frequency of the response is usually called the loop bandwidth,
This smooths the current pulses into a voltage which in turn drives BW. Large loop bandwidths result in very fast transient response.
the VCO. The VCO frequency will then increase or decrease as However, this is not always advantageous, as we shall see in
necessary, by KV DV, where KV is the VCO sensitivity in MHz/ Part 2, since there is a tradeoff between fast transient response
Volt and DV is the change in VCO input voltage. This will continue and reference spur attenuation.
until e(s) is zero and the loop is locked. The charge pump and
VCO thus serves as an integrator, seeking to increase or decrease PLL APPLICATIONS TO FREQUENCY UPSCALING
its output frequency to the value required so as to restore its input The phase-locked loop allows stable high frequencies to be
(from the phase detector) to zero. generated from a low-frequency reference. Any system that
requires stable high frequency tuning can benefit from the
PLL technique. Examples of these applications include
VCO Output Frequency (MHz)

wireless base stations, wireless handsets, pagers, CATV

systems, clock-recovery and -generation systems. A good
example of a PLL application is a GSM handset or base station.
Figure 4 shows the receive section of a GSM base station.
∆F In the GSM system, there are 124 channels (8 users per channel)
KV = ∆F/∆V
of 200-kHz width in the RF band. The total bandwidth occupied
is 24.8 MHz, which must be scanned for activity. The handset has
∆V a transmit (Tx) range of 880 MHz to 915 MHz and a receive (Rx)
range of 925 MHz to 960 MHz. Conversely, the base station has a
Tx range of 925 MHz to 960 MHz and an Rx range of 880 MHz
VCO Tuning Voltage (Volts)
to 915 MHz. For this example, we will consider just the base station
Figure 3. VCO transfer function. transmit and receive sections. The frequency bands for GSM900
The overall transfer function (CLG or Closed-Loop Gain) of the and DCS1800 Base Station Systems are shown in Table 1. Table 2
PLL can be expressed simply by using the CLG expression for a shows the channel numbers for the carrier frequencies (RF
negative feedback system as given above. channels) within the frequency bands of Table 1. Fl(n) is the center
frequency of the RF channel in the lower band (Rx) and Fu(n) is
the corresponding frequency in the upper band (Tx).
FO Forward Gain Table 1. Frequency Bands for GSM900 and DCS1800 Base
=
FREF 1 + Loop Gain Station Systems

Forward Gain , G =
K D KV Z s () TX RX
s P-GSM900 935 to 960 MHz 890 to 915 MHz

()
DCS1800 1805 to 1880 MHz 1710 to 1785 MHz
K D KV Z s
Loop Gain , GH = E-GSM900 925 to 960 MHz 880 to 915 MHz
Ns

Table 2. Channel Numbering for GSM900 and DCS1800 Base Station Systems
RX TX
PGSM900 Fl(n) = 890 + 0.2 × (n) 1 ≤ n ≤ 124 Fu(n) = Fl(n) + 45
EGSM900 Fl(n) = 890 + 0.2 × (n) 0 ≤ n ≤ 124 Fu(n) = Fl(n) + 45
Fl(n) = 890 + 0.2 × (n – 1024) 975 ≤ n ≤ 1023
DCS1800 Fl(n) = 1710.2 + 0.2 × (n – 512) 512 ≤ n ≤ 885 Fu(n) = Fl(n) + 95

2 Analog Dialogue 33-3 (© 1999 Analog Devices)

 900MHz
RF
-104dBm to -
60dBm
TCXO 13MHz

VCO Synthesizer Synthesizer VCO

640MHz to 229.3MHz
675MHz

L0 1 1ST IF L0 2 2ND IF
Tuned 240 MHz Fixed 10.7 MHz
Demodulator

Figure 4. Signal chain for GMS base-station receiver.

The 900-MHz RF input is filtered, amplified and applied to the It is worth noting that, in addition to the tunable RF LO, the
first stage mixer. The other mixer input is driven from a tuned receiver section also uses a fixed IF (in the example shown this is
local oscillator (LO). This must scan the input frequency range to 240 MHz). Even though frequency tuning is not needed on this
search for activity on any of the channels. The actual implementa- IF, the PLL technique is still used. The reason for this is that it is
tion of the LO is by means of the PLL technique already described. an affordable way of using the stable system reference frequency
If the 1st intermediate-frequency (IF) stage is centered at to produce the high frequency IF signal. Several synthesizer
240 MHz, then the LO must have a range of 640 MHz to 675 MHz manufacturers recognize this fact by offering dual versions of the
in order to cover the RF input band. When a 200-kHz reference devices: one operating at the high RF frequency (>800 MHz) and
frequency is chosen, it will be possible to sequence the VCO output one operating at the lower IF frequency (500 MHz or less).
through the full frequency range in steps of 200 kHz. For example, On the transmit side of the GSM system, similar requirements
when an output frequency of 650 MHz is desired, N will have a exist. However, it is more common to go directly from baseband
value of 3250. This 650-MHz LO will effectively check the 890- to the final RF in the Transmit section; this means that the typical
MHz RF channel (FRF – FLO = FIF or FRF = FLO + FIF). When N TX VCO for a base station has a range of 925 MHz to 960 MHz
is incremented to 3251, the LO frequency will now be 650.2 MHz (RF band for the Transmit section).
and the RF channel checked will be 890.2 MHz. This is shown
graphically in Figure 5. CIRCUIT EXAMPLE
Figure 6 shows an actual implementation of the local oscillator
GSM Example
for the transmit section of a GSM handset. We are assuming direct
baseband to RF up-conversion. This circuit uses the new ADF4111
PLL Frequency Synthesizer from ADI and the VCO190-902T
Voltage Controlled Oscillator from Vari-L Corporation (http://
www.vari-L.com/).
The reference input signal is applied to the circuit at FREFIN and
is terminated in 50 Ω. This reference input frequency is typically
13 MHz in a GSM system. In order to have a channel spacing of
(N-1)FREF (N)FREF (N+1)FREF 200 kHz (the GSM standard), the reference input must be divided
by 65, using the on-chip reference divider of the ADF4111.
∆F = FREF
For GSM: FREF = 200 kHz The ADF4111 is an integer-N PLL frequency synthesizer, capable
FRF = 880MHz to 915MHz for the Receiver
of operating up to an RF frequency of 1.2 GHz. In this integer-N
If First IF is at 240MHz then LO must go from
type of synthesizer, N can be programmed from 96 to 262,000 in
640MHz to 675MHz.
discrete integer steps. In the case of the handset transmitter, where
This Means N must vary from 3200 to 3375
an output range of 880 MHz to 915 MHz is needed, and where
the internal reference frequency is 200 kHz, the desired N values
Figure 5. Testing frequencies for GSM base-station receiver. will range from 4400 to 4575.

Analog Dialogue 33-3 (© 1999 Analog Devices) 3

The charge pump output of the ADF4111 (Pin 2) drives the loop The ADF4111 uses a simple 4-wire serial interface to com-
filter. This filter (Z(s) in Figure 2) is basically a 1st-order lag-lead municate with the system controller. The reference counter, the N
type. In calculating the loop filter component values, a number of counter and various other on-chip functions are programmed via
items need to be considered. In this example, the loop filter was this interface.
designed so that the overall phase margin for the system would be
45 degrees. Other PLL system specifications are given below: CONCLUSION
KD = 5 mA In this first part of the series, we have introduced the basic concepts
KV = 8.66 MHz/V of PLLs with simple block diagrams and equations. We have shown
Loop Bandwidth = 12 kHz a typical example of where the PLL structure is used and given a
FREF = 200 kHz detailed description of a practical implementation.
N = 4500 In the next installment, we will delve deeper into the speci-
Extra Reference Spur Attenuation = 10 dB fications which are critical to PLLs and discuss their system
All of these specifications are needed and used to come up with implications.
the loop filter components values shown in Figure 6.
REFERENCES
The loop filter output drives the VCO, which, in turn, is fed back 1. Mini-Circuits Corporation, “VCO Designers Handbook.”
to the RF input of the PLL synthesizer and also drives the RF
Output terminal. A T-circuit configuration with 18-ohm resistors 2. L.W. Couch, “Digital and Analog Communications Systems”
is used to provide 50-ohm matching between the VCO output, the Macmillan Publishing Company, New York.
RF output and the RFIN terminal of the ADF4111. 3. P. Vizmuller, “RF Design Guide,” Artech House.
In a PLL system, it is important to know when the system is in 4. R.L. Best, “Phase Locked Loops: Design, Simulation and
lock. In Figure 6, this is accomplished by using the MUXOUT Applications,” 3rd Edition, McGraw Hill. b
signal from the ADF4111. The MUXOUT pin can be pro-
grammed to monitor various internal signals in the synthesizer.
One of these is the LD or lock-detect signal. When MUXOUT is
chosen to select lock detect, it can be used in the system to trigger
the output power amplifier, for example.

VDD VP
RFOUT

100 pF

7 15 16 14
3.3 kΩ 100 pF 18 Ω 18 Ω
AVDD DVDD VP VCC
1000 pF 1000 pF 2 2 10
8 CP
FREFIN REFIN VCO190-902T
1 nF 18 Ω
51 Ω ADF4111 5.6 kΩ
620 pF

1, 3, 4, 5, 7, 8,
9, 11, 12, 13
8.2 nF

14 Lock
CE MUXOUT
CLK Detect
DATA 100 pF
LE 6
RFINA
5
SPI Compatible Serial Bus

RFINB
51 Ω
CPGND

AGND

DGND

3 4 9 100 pF

Decoupling Capacitors (0.1 µF/10 pF) on AVDD, DVDD, VP of the ADF4111

and on VCC of the VCO190-902T have been omitted from the diagram to aid
clarity.

Figure 6. Transmitter local oscillator for GSM handset.

4 Analog Dialogue 33-3 (© 1999 Analog Devices)