Datasheet MAX2620E-D, MAX2620EUA Datasheet (Maxim)

MAX2620

1

VCC1

TANK

FDBK

SHDN

2

3

4

8

OUT

VCC2

GND

OUT

7

6

5

V

CC

V

CC

V

CC

V

CC

BIAS

SUPPLY

C17

1.5pF

C5

C6

1000pF

1000pF

1000pF

10Ω

CERAMIC

RESONATOR

L1

V

TUNE

900MHz BAND OSCILLATOR

1k

D1

ALPHA

SMV1204-34

1.5pF 1.5pF

51Ω

10nH

C3

2.7pF

C4
1pF

0.1µF

1000pF

OUT TO SYNTHESIZER

OUT TO MIXER

SHDN

MAX2620

10MHz to 1050MHz Integrated

RF Oscillator with Buffered Outputs

________________________________________________________________

Maxim Integrated Products

1

19-1248; Rev 1; 5/98

EVALUATION KIT

AVAILABLE

_________________General Description

The MAX2620 combines a low-noise oscillator with two
output buffers in a low-cost, plastic surface-mount,
ultra-small µMAX package. This device integrates func­tions typically achieved with discrete components. The
oscillator exhibits low phase noise when properly
mated with an external varactor-tuned resonant tank
circuit. Two buffered outputs are provided for driving
mixers or prescalers. The buffers provide load isolation
to the oscillator and prevent frequency pulling due to
load-impedance changes. Power consumption is typi­cally just 27mW in operating mode (VCC= 3.0V), and
drops to less than 0.3µW in standby mode. The MAX2620
operates from a single +2.7V to +5.25V supply.

________________________Applications

Analog Cellular Phones
Digital Cellular Phones
900MHz Cordless Phones
900MHz ISM-Band Applications
Land Mobile Radio
Narrowband PCS (NPCS)

____________________________Features

♦ Low-Phase-Noise Oscillator: -110dBc/Hz

(25kHz offset from carrier) Attainable

♦ Operates from Single +2.7V to +5.25V Supply
♦ Low-Cost Silicon Bipolar Design
♦ Two Output Buffers Provide Load Isolation
♦ Insensitive to Supply Variations
♦ Low, 27mW Power Consumption (V

CC

= 3.0V)

♦ Low-Current Shutdown Mode: 0.1µA (typ)

PART

MAX2620EUA -40°C to +85°C

TEMP. RANGE PIN-PACKAGE

8 µMAX

_______________Ordering Information

For free samples & the latest literature: http://www.maxim-ic.com, or phone [phone].
For small orders, phone [phone] ext. 3468.

MAX2620E/D -40°C to +85°C Dice*

Pin Configuration appears at end of data sheet.

*

Dice are tested at TA= +25°C, DC parameters only.

____________________________________________________Typical Operating Circuit

MAX2620

10MHz to 1050MHz Integrated
RF Oscillator with Buffered Outputs

2 _______________________________________________________________________________________

ABSOLUTE MAXIMUM RATINGS

DC ELECTRICAL CHARACTERISTICS

(VCC1, VCC2 = +2.7V to +5.25V, FDBK = open, TANK = open, OUT and OUT connected to VCCthrough 50Ω, SHDN = 2V,

T

A

= -40°C to +85°C, unless otherwise noted. Typical values measured at VCC1 = VCC2 = 3.0V, TA= +25°C.) (Note 1)

AC ELECTRICAL CHARACTERISTICS

(Per Test Circuit of Figure 1, VCC= +3.0V, SHDN = VCC, Z

LOAD

= Z

SOURCE

= 50Ω, PIN= -20dBm (50Ω), f

TEST

= 900MHz,

T

A

= +25°C, unless otherwise noted.)

Stresses beyond those listed under “Absolute Maximum Ratings” may cause permanent damage to the device. These are stress ratings only, and functional
operation of the device at these or any other conditions beyond those indicated in the operational sections of the specifications is not implied. Exposure to
absolute maximum rating conditions for extended periods may affect device reliability.

VCC1, VCC2 to GND................................................-0.3V to +6V

TANK, SHDN to GND.................................-0.3V to (V

CC

+ 0.3V)

OUT, OUT to GND...........................(V

CC

- 0.6V) to (VCC+ 0.3V)

FDBK to GND..................................(V

CC

- 2.0V) to (VCC+ 0.3V)

Continuous Power Dissipation (T

A

= +70°C)

µMAX (derate 5.7mW/°C above +70°C) .....................457mW

Operating Temperature Range

MAX2620EUA.................................................-40°C to +85°C

Junction Temperature......................................................+150°C

Storage Temperature Range.............................-65°C to +165°C

Lead Temperature (soldering, 10sec).............................+300°C

µA

0.1 2

SHDN = 0.6V

Shutdown Current

mA9.0 12.5

UNITSMIN TYP MAXCONDITIONSPARAMETER

Supply Current

V2.0Shutdown Input Voltage High
V0.6Shutdown Input Voltage Low

µA

5.5 20

SHDN = 2.0V

Shutdown Bias Current High

µA

0.5

SHDN = 0.6V

Shutdown Bias Current Low

MHz10 1050TA= -40°C to +85°C (Note 2)

UNITSMIN TYP MAXCONDITIONSPARAMETER

Frequency Range

dB50

OUT or OUT to TANK; OUT, OUT driven at P = -20dBm

Reverse Isolation

dB33

OUT to OUT

Output Isolation

Note 2: Guaranteed by design and characterization at 10MHz, 650MHz, 900MHz, and 1050MHz. Over this frequency range, the

magnitude of the negative real impedance measured at TANK is greater than one-tenth the magnitude of the reactive
impedances at TANK. This implies proper oscillator start-up when using an external resonator tank circuit with Q > 10. C3
and C4 must be tuned for operation at the desired frequency.

Note 1: Specifications are production tested and guaranteed at T

A

= +25°C and TA= +85°C. Specifications are guaranteed by

design and characterization at T

A

= -40°C.

MAX2620

10MHz to 1050MHz Integrated

RF Oscillator with Buffered Outputs

_______________________________________________________________________________________ 3

TYPICAL OPERATING CIRCUIT PERFORMANCE—900MHz Band Ceramic­Resonator-Based Tank

(Per Typical Operating Circuit, VCC= +3.0V, V

TUNE

= 1.5V, SHDN = V

CC,

load at OUT = 50Ω, load at OUT = 50Ω, L1 = coaxial

ceramic resonator: Trans-Tech SR8800LPQ1357BY, C6 = 1pF, T

A

= +25°C, unless otherwise noted.)

-110

SSB @ ∆f = 25kHz

MHz±13V

TUNE

= 0.5V to 3.0V

UNITSMIN TYP MAXCONDITIONSPARAMETER

Tuning Range

dBc/Hz

-132

SSB @ ∆f = 300kHz

Phase Noise

-6 -2At OUT (Note 2)

dBc-29Second-Harmonic Output

MHz/V11Average Tuning Gain

kHzp-p163VSWR = 1.75:1, all phasesLoad Pull
kHz/V71VCCstepped from 3V to 4VSupply Pushing

Note 3: Guaranteed by design and characterization.

dBm/Hz-147fO± >10MHzNoise Power

-11 -8

At OUT, per test circuit of Figure 1; TA= -40°C to +85°C
(Note 3)

dBm

-16 -12.5

At OUT (Note 3)

Output Power (single-ended)

TYPICAL OPERATING CIRCUIT PERFORMANCE—900MHz Band Inductor-Based Tank

(Per Typical Operating Circuit, VCC= +3.0V, V

TUNE

= 1.5V, SHDN = V

CC,

load at OUT = 50Ω, load at OUT = 50Ω, L1 = 5nH

(Coilcraft A02T), C6 = 1.5pF, T

A

= +25°C, unless otherwise noted.)

MHz/V13Average Tuning Gain

dBm/Hz-147fO± >10MHzNoise Power

kHzp-p340VSWR = 1.75:1, all phase anglesLoad Pull
kHz/V150VCCstepped from 3V to 4VSupply Pushing

-11 -8

At OUT, per test circuit of Figure 1; TA= -40°C to +85°C
(Note 3)

dBm

-16 -12.5

At OUT (Note 3)

Output Power (single-ended)

-107

SSB @ ∆f = 25kHz

MHz±15V

TUNE

= 0.5V to 3.0V

UNITSMIN TYP MAXCONDITIONSPARAMETER

Tuning Range

dBc/Hz

-127

SSB @ ∆f = 300kHz

Phase Noise

-6 -2At OUT (Note 2)

dBc-29Second-Harmonic Output

Note 3: Guaranteed by design and characterization.

MAX2620

10MHz to 1050MHz Integrated
RF Oscillator with Buffered Outputs

4 _______________________________________________________________________________________

__________________________________________Typical Operating Characteristics

(Per test circuit of Figure 1, VCC= +3.0V, SHDN = VCC, Z

LOAD

= Z

SOURCE

= 50Ω, PIN= -20dBm/50Ω, f

TEST

= 900MHz, TA= +25°C,

unless otherwise noted.)

-5

B

C

0

A:
B:

C:

10MHz BAND CIRCUIT
NOT CHARACTERIZED FOR THIS FREQUENCY BAND.
EXPECTED PERFORMANCE SHOWN.
900MHz BAND CIRCUIT

200 400 600 800 1000 1200

OUT OUTPUT POWER vs. FREQUENCY

OVER V

CC

AND TEMPERATURE

-7

MAX2620-01

FREQUENCY (MHz)

POWER (dBm)

-9

-6

-8

TA = +85°C
T

A

= +25°C

T

A

= -40°C

V

CC

= 5.25V

V

CC

= 5.25V

V

CC

= 2.7V

V

CC

= 2.7V

A

-13.0

-13.5

-12.0

-12.5

-11.0

-11.5

0 400200 600 800 1000 1200

OUT OUTPUT POWER vs. FREQUENCY

OVER V

CC

AND TEMPERATURE

MAX2620-02

FREQUENCY (MHz)

POWER (dBm)

V

CC

= 5.25V

V

CC

= 2.7V

TA = +85°C

T

A

= +25°C

T

A

= -40°C

FREQUENCY

(MHz)

REAL COMPONENT

(R in Ω)

IMAGINARY COMPONENT

(X in Ω)

250 106 163
350 68 102
450 60 96
550 35 79

1050 6.5 22.7

Table 1. Recommended Load Impedance at OUT or OUT for
Optimum Power Transfer

850

650 17.5 62.3
750 17.2 50.6

10.9 33.1

950 7.3 26.3

MAX2620

10MHz to 1050MHz Integrated

RF Oscillator with Buffered Outputs

_______________________________________________________________________________________ 5

900MHz BAND CIRCUIT*

TYPICAL 1/S11 vs. FREQUENCY

MEASURED AT TEST PORT

MAX2620-04

650MHz
84 + j142

800MHz
49 + j105

900MHz
36 + j90

1050MHz
21 + j78

*SEE FIGURE 1

10MHz BAND CIRCUIT

TYPICAL 1/S11 vs. FREQUENCY

MEASURED AT TEST PORT

MAX2620-05

5MHz
262 + j261

10MHz

63.6 + j121.5

15MHz
28 + j79.8

C3 = C4 = 270pF
L3 = 10µH
C2 = C10 = C13 = 0.01µF

10.0

7.0

-40

SUPPLY CURRENT

vs. TEMPERATURE

9.0

MAX2620-06

TEMPERATURE (°C)

SUPPLY CURRENT (mA)

8.0

7.5

9.5

8.5

-20 0 20 40 60 80 100

VCC = 2.7V

VCC = 5.25V

-90

-80

-70

-60

-50

-30

-40

-20

-10

0

50 250 450 650 850 1050

REVERSE ISOLATION vs. FREQUENCY

MAX2620-03

FREQUENCY (MHz)

REVERSE ISOLATION (dB)

VCC = 2.7V TO 5.25V
C3, C4 REMOVED

_____________________________Typical Operating Characteristics (continued)

(Per

Typical Operating Circuit

, VCC= +3.0V, V

TUNE

= 1.5V, SHDN = V

CC,

load at OUT = 50Ω, load at OUT = 50Ω, L1 = coaxial

ceramic resonator: Trans-Tech SR8800LPQ1357BY, C6 = 1pF, T

A

= +25°C, unless otherwise noted.)

MAX2620

10MHz to 1050MHz Integrated
RF Oscillator with Buffered Outputs

6 _______________________________________________________________________________________

_______________________________________________________________Pin Description

NAME FUNCTIONPIN

3 FDBK

Oscillator Feedback Circuit Connection. Connecting capacitors of the appropriate value between FDBK and
TANK and between FDBK and GND tunes the oscillator’s reflection gain (negative resistance) to peak at the
desired oscillation frequency. Refer to the

Applications Information

section.

2 TANK Oscillator Tank Circuit Connection. Refer to the

Applications Information

section.

1 VCC1

Oscillator DC Supply Voltage. Decouple VCC1 with 1000pF capacitor to ground. Use a capacitor with low
series inductance (size 0805 or smaller). Further power-supply decoupling can be achieved by adding a
10Ω resistor in series from VCC1 to the supply. Proper power-supply decoupling is critical to the low noise
and spurious performance of any oscillator.

8 OUT

Open-Collector Output Buffer. Requires external pull-up to the voltage supply. Pull-up can be resistor,
choke, or inductor (which is part of a matching network). The matching-circuit approach provides the high­est-power output and greatest efficiency. Refer to Table 1 and the

Applications Information

section. OUT

may be used with OUT in a differential output configuration.

7 VCC2

Output Buffer DC Supply Voltage. Decouple VCC2 with a 1000pF capacitor to ground. Use a capacitor with
low series inductance (size 0805 or smaller).

6 GND Ground Connection. Provide a low-inductance connection to the circuit ground plane.

5

OUT

Open-Collector Output Buffer (complement). Requires external pull-up to the voltage supply. Pull-up can be
resistor, choke, or inductor (which is part of a matching network). The matching-circuit approach provides
the highest-power output and greatest efficiency. Refer to Table 1 and the

Applications Information

section.

OUT may be used with OUT in a differential output configuration.

4

SHDN

Logic-Controlled Input. A low level turns off the entire circuitry such that the IC will draw only leakage current
at its supply pins. This is a high-impedance input.

_____________________________Typical Operating Characteristics (continued)

(Per

Typical Operating Circuit

, VCC= +3.0V, V

TUNE

= 1.5V, SHDN = V

CC,

load at OUT = 50Ω, load at OUT = 50Ω, L1 = coaxial

ceramic resonator: Trans-Tech SR8800LPQ1357BY, C6 = 1pF, T

A

= +25°C, unless otherwise noted.)

-114

-112

-110

-108

-106

-104

-40 -20 0 20 40 60 80

PHASE NOISE vs. TEMPERATURE

MAX2620-07

TEMPERATURE (°C)

SSB PHASE NOISE (dBc/Hz)

SSB @ ∆f = 25kHz

L1 = 5nH INDUCTOR
C6 = 1.5pF

L1 = COAXIAL CERAMIC RESONATOR
(TRANS-TECH SR8800LPQ1357BY)
C6 = 1pF

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

0 1.3 2.6 3.9 5.2 6.5

OUTPUT SPECTRUM

FUNDAMENTAL NORMALIZED TO 0dB

MAX2620-08

FREQUENCY (GHz)

RELATIVE OUTPUT LEVEL (dBc)

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

0.1 10 1000100

SINGLE SIDEBAND PHASE NOISE

MAX2620-09

OFFSET FREQUENCY (kHz)

SSB PHASE NOISE (dBc/Hz)

1

L1 = 5nH INDUCTOR
C6 = 1.5pF

L1 = COAXIAL
CERAMIC RESONATOR
(TRANS-TECH
SR8800LPQ1357BY)
C6 = 1pF

MAX2620

10MHz to 1050MHz Integrated

RF Oscillator with Buffered Outputs

_______________________________________________________________________________________ 7

_______________Detailed Description

Oscillator

The oscillator is a common-collector, negative­resistance type that uses the IC’s internal parasitic ele­ments to create a negative resistance at the base­emitter port. The transistor oscillator has been opti­mized for low-noise operation. Base and emitter leads
are provided as external connections for a feedback
capacitor and resonator. A resonant circuit, tuned to
the appropriate frequency and connected to the base
lead, will cause oscillation. Varactor diodes may be
used in the resonant circuit to create a voltage-con­trolled oscillator (VCO). The oscillator is internally
biased to an optimal operating point, and the base and
emitter leads need to be capacitively coupled due to
the bias voltages present.

Output Buffers

The output buffers (OUT and OUT) are an open­collector, differential-pair configuration and provide
load isolation to the oscillator. The outputs can be used
differentially to drive an integrated circuit mixer.
Alternatively, isolation is provided between the buffer
outputs when one output drives a mixer (either upcon­version or downconversion) and the other output drives
a prescaler. The isolation in this configuration prevents
prescaler noise from corrupting the oscillator signal’s
spectral purity.

A logic-controlled SHDN pin turns off all bias to the IC
when pulled low.

__________Applications Information

Design Principles

At the frequency of interest, the MAX2620 portion of
Figure 2 shows the one-port circuit model for the TANK
pin (test port in Figure 1).

For the circuit to oscillate at a desired frequency, the res­onant tank circuit connected to TANK must present an
impedance that is a complement to the network
(Figure 2). This resonant tank circuit must have a positive
real component that is a maximum of one-half the magni­tude of the negative real part of the oscillator device, as
well as a reactive component that is opposite in sign to
the reactive component of the oscillator device.

-R

n

LESS THAN 1/2

TIMES R

L

-jX

T

TANK

jX

L

RESONANT
TANK

OSCILLATOR
DEVICE

Figure 2. Simplified Oscillator Circuit Model

MAX2620

1

2

VCC1

TANK

FDBK

SHDN

3

4

8

OUT

VCC2

OUT

GND

7

6

5

V

CC

V

CC

V

CC

V

CC

V

CC

TEST PORT

BIAS

SUPPLY

C13*

1000pF

C2*

1000pF

ON

OFF

1000pF

1000pF

1000pF

10Ω

10Ω

L3*

220nH

51Ω

C3*

2.7pF
C4*

1pF

1000pF

1000pF

C10*

1000pF

Z

O

= 50Ω

*AT 10MHz, CHANGE TO:
C3 = C4 = 270pF
L3 = 10µH
C2 = C10 = C13 = 0.01µF

Z

O

= 50Ω

OUT

OUT

Figure 1. 900MHz Test Circuit

MAX2620

10MHz to 1050MHz Integrated
RF Oscillator with Buffered Outputs

8 _______________________________________________________________________________________

Keeping the resonant tank circuit’s real component less
than one-half the magnitude of the negative real com­ponent ensures that oscillations will start. After start-up,
the oscillator’s negative resistance decreases, primarily
due to gain compression, and reaches equilibrium with
the real component (the circuit losses) in the resonant
tank circuit. Making the resonant tank circuit reactance
tunable (e.g., through use of a varactor diode) allows
for tuneability of the oscillation frequency, as long as
the oscillator exhibits negative resistance over the
desired tuning range. See Figures 3 and 4.

The negative resistance of the MAX2620 TANK pin can
be optimized at the desired oscillator frequency by
proper selection of feedback capacitors C3 and C4.
For example, the one-port characteristics of the device
are given as a plot of 1/S11 in the

Typical Operating

Characteristics

. 1/S11 is used because it maps inside
the unit circle Smith chart when the device exhibits
negative resistance (reflection gain).

V

TUNE

V

CC

VCC1

TANK

FDBK

SHDN

8

7

6

5

OUT

VCC2

GND

OUT

1

2

3

4

V

CC

V

CC

V

CC

1k

D1

D1 = SMV1200-155 DUAL VARACTOR

C17
33pF

10Ω

51Ω

0.01µF

10µH

0.01µF

OUT TO
MIXER

C6
33pH

C5

150pF

C3
270pF

1000pF

1000pF

1000pF

27pF

1000pF

C4
270pF

SHDN

L1

2.2µH

OUT TO
SYNTHESIZER

MAX2620

Figure 3. 10MHz VCO LC Resonator

MAX2620

10MHz to 1050MHz Integrated

RF Oscillator with Buffered Outputs

_______________________________________________________________________________________ 9

Example Calculation

According to the electrical model shown in Figure 5, the
resonance frequency can be calculated as:
[Equation 1]

R

n

, the negative real impedance, is set by C3 and C4

and is approximately:
[Equation 2]

where gm= 0.018mS.
Using the circuit model of Figure 5, the following exam-

ple describes the design of an oscillator centered at
900MHz.

Choose: L1 = 5nH ±10%

Q = 140

Calculate R

p

= Q x 2π x f x L1

Using Equation 1, solve for varactor capacitance (CD1).
CD1is the capacitance of the varactor when the volt­age applied to the varactor is approximately at half­supply (the center of the varactor’s capacitance range).
Assume the following values:

C

STRAY

= 2.7pF, C17 = 1.5pF, C6 = 1.5pF, C5 = 1.5pF,
C3 = 2.7pF, and C4 = 1pF.
The value of C

STRAY

was based on approximate perfor­mance of the MAX2620 EV kit. Values of C3 and C4 are
chosen to minimize Rn(Equation 2) while not loading
the resonant circuit with excessive capacitance.

The varactor’s capacitance range should allow for the
desired tuning range. Across the tuning frequency
range, ensure that Rp< 1/2 Rn.

The MAX2620’s oscillator is optimized for low-phase­noise operation. Achieving lowest phase-noise charac­teristics requires the use of high-Q (quality factor)
components such as ceramic transmission-line type
resonators or high-Q inductors. Also, keep C5 and C17

R g

fC fC

n m

=





















1

2 312 4π π

V

CC

VCC1

TANK

FDBK

SHDN

8

7

6

5

OUT

VCC2

GND

OUT

1

2

3

4

V

CC

V

CC

V

CC

10Ω

51Ω

0.01µF

10µH

0.01µF

OUT

30pF

120pF

120pF

0.01µF

0.01µF

0.01µF

27pF

0.01µF

SHDN

OUT

MAX2620

X = STATEK AT-3004 10MHz
FUNDAMENTAL MODE CRYSTAL SURFACE MOUNT
C

LOAD

= 20pF

Figure 4. 10MHz Crystal Oscillator

f

1

2 L1 C +

C x C

C + C

C

C C C C

C C C C

O

STRAY

17 D1

17 D1

6

3 03 4 04

3 03 4 04

=

+ +

+

( )+( )

+ + +















π

MAX2620

10MHz to 1050MHz Integrated
RF Oscillator with Buffered Outputs

10 ______________________________________________________________________________________

(see

Typical Operating Circuit

) as small a value as pos­sible while still maintaining desired frequency and tun­ing range to maximize loaded Q.

There are many good references on the topic of oscilla­tor design. An excellent reference is “The Oscillator
as a Reflection Amplifier, an Intuitive Approach to
Oscillator Design,” by John W. Boyles,

Microwave

Journal

, June 1986, pp. 83–98.

Output Matching Configuration

Both of the MAX2620’s outputs (OUT and OUT) are
open collectors. They need to be pulled up to the sup­ply by external components. An easy approach to this
pull-up is a resistor. A 50Ω resistor value would inher­ently match the output to a 50Ω system. The

Typical

Operating Circuit

shows OUT configured this way.
Alternatively, a choke pull-up (Figure 1), yields greater
output power (approximately -8dBm at 900MHz).

When maximum power is required, use an inductor as
the supply pull-up, and match the inductor’s output
impedance to the desired system impedance. Table 1
in the

Typical Operating Characteristics

shows recom-

mended load impedance presented to OUT and OUT

for maximum power transfer. Using this data and stan­dard matching-network synthesis techniques, a match­ing network can be constructed that will optimize power
output into most load impedances. The value of the
inductor used for pull-up should be used in the synthe­sis of the matching network.

1
2
3
4

8
7
6
5

OUT
VCC2
GND

OUT

SHDN

FDBK

TANK

VCC1

MAX2620

µMAX

TOP VIEW

__________________Pin Configuration

MAX2620

C5

C6

R

p

L1

R

n

C3

INDUCTOR
OR
CERAMIC
RESONATOR

VARACTOR+
COUPLING

TEST PORT
MEASUREMENT
(FIGURE 1)

RESONANT TANK MODEL

MAX2620 PACKAGE MODEL

PCB
PARASITICS

C4

C

04

2.4pF

C

03

2.4pF

C17

C

D1

C

STRAY

Figure 5. Electrical Model of MAX2620 Circuit

MAX2620

10MHz to 1050MHz Integrated

RF Oscillator with Buffered Outputs

______________________________________________________________________________________ 11

________________________________________________________Package Information

8LUMAXD.EPS

MAX2620

10MHz to 1050MHz Integrated
RF Oscillator with Buffered Outputs

12 ______________________________________________________________________________________

NOTES