Additional Information
Introduction
This application note presents three voltagecontrolled oscillator (VCO) designs for popular IF frequencies of 130MHz, 165MHz, and 380MHz. These designs reduce the number of iterations required for optimized results. Analysis can be accomplished with a simple spreadsheet program.
VCO Design
Figure 2 shows the differential tank circuit used for the MAX2360 IF VCO.For analysis purposes, the tank circuit must be reduced to an equivalent simplified model.
Figure 1 depicts the basic VCO model. The frequency of oscillation can be characterized by EQN1:

EQN1

f
_{osc} = frequency of oscillation
L = inductance of the coil in the tank circuit
C
_{int} = internal capacitance of the MAX2360 tank port
C
_{t} = total equivalent capacitance of the tank circuit
Figure 1. Basic VCO model.
R
_{n} = equivalent negative resistance of the MAX2360 tank port
C
_{int} = internal capacitance of the MAX2360 tank port
C
_{t} = total equivalent capacitance of the tank circuit
L = inductance of the coil in the tank circuit
Figure 2. The MAX2360 tank circuit.
Inductor L resonates with the total equivalent capacitance of the tank and the internal capacitance of the oscillator (C
_{t} + C
_{int}) (see Figure 1). C
_{coup} provides DC block and couples the variable capacitance of the varactor diodes to the tank circuit. C
_{cent} is used to center the tank's oscillationfrequency to a nominal value. It is not required but adds a degree of freedom by allowing you to finetune resonance between inductor values. Resistors (R) provide reversebias voltage to the varactor diodes via the tune voltage line (V
_{tune}). Their value should be chosen large enough so as not to affect loaded tank Q but small enough so that 4kTBR noise is negligible. The resistors' noise voltage gets modulated by K
_{vco}, producing phase noise. Capacitance C
_{V} is the variable tuning component in the tank. The capacitance of the varactor diode (C
_{V}) is a function of reversebias voltage (see Appendix A for the varactor model). V
_{tune} is the tuning voltage from a phaselocked loop (PLL).
Figure 3 shows the lumped C
_{stray} VCO model. Parasitic capacitance and inductance plague every RF circuit. In order to predict the frequency of oscillation, the parasitic elements must be taken into account. The circuit in Figure 3 lumps the parasitic elements in one capacitor called C
_{stray}. The frequency of oscillation can be characterized by EQN2:

EQN2

L = inductance of the coil in the tank circuit
C
_{int} = internal capacitance of the MAX2360 tank port
C
_{cent} = tank capacitor used to center oscillation frequency
C
_{stray} = lumped stray capacitance
C
_{coup} = tank capacitor used to couple the varactor to the tank
C
_{V} = net variable capacitance of the varactor diode (including series inductance)
C
_{vp} = varactor pad capacitance
Figure 3. Lumped C_{stray} model.
Figure 4 depicts the detailed VCO model. It takes into account the capacitance of the pads but does not include the effects of series inductance for simplicity. C
_{stray} is defined as:

EQN3

C
_{L} = capacitance of the inductor
C
_{LP} = capacitance of inductor pads
C
_{DIFF} = capacitance due to parallel traces
Figure 4. Detailed VCO model.
R
_{n} = equivalent negative resistance of the MAX2360 tank port
C
_{int} = internal capacitance of the MAX2360 tank port
L
_{T} = inductance of series trace to the inductor tank circuit
C
_{DIFF} = capacitance due to parallel traces
L = inductance of the coil in the tank circuit
C
_{L} = capacitance of the inductor
C
_{LP} = capacitance of inductor pads
C
_{cent} = tank capacitor used to center oscillation frequency
C
_{coup} = tank capacitor used to couple the varactor to the tank
C
_{var} = variable capacitance of the varactor diode
C
_{vp} = varactor pad capacitance
L
_{S} = series inductance of the varactor
R = resistance of varactor reversebias resistors
To simplify analysis, inductance L
_{T} is ignored in this design. The effects of L
_{T} are more pronounced at higher frequencies. To mathematically model the shift in frequency due to L
_{T} with the spreadsheets that follow, the value of C
_{DIFF} can be increased appropriately. Minimize inductance L
_{T} to prevent undesired series resonance. This can be accomplished by making the traces short.
Tuning Gain
Tuning gain (K
_{vco}) must be minimized for best closedloop phase noise. Resistors in the loop filter as well as the resistors "R" (Figure 2) will produce broadband noise. Broadband thermal noise (
) will modulate the VCO by K
_{vco}, which is measured in MHz/V. There are two ways to minimize K
_{vco}. One is to minimize the frequency range over which the VCO must tune. The second way is to maximize the tuning voltage available. To minimize the frequency range over which the VCO must tune, tight tolerance components must be used, as will be shown. To maximize tuning voltage, a charge pump with a large compliance range is needed. This is usually accomplished by using a larger V
_{cc}. The compliance range for the MAX2360 is 0.5V to Vcc0.5V. In batterypowered applications, the compliance range is usually fixed by the battery voltage or regulator.
Basic Concept for Trimless Design
VCO design manufacturability with realworld components will require an error budget analysis. In order to design a VCO to oscillate at a fixed frequency (f
_{osc}), the tolerance of components must be taken into consideration. Tuning gain (K
_{vco}) must be designed into the VCO to account for these component tolerances. The tighter the component tolerance, the smaller the tuning gain and the lower the closedloop phase noise. For the worstcase error budget design, we will look at three VCO models:
1. Maximumvalue components (EQN5)
2. Nominal tank, all components perfect (EQN2)
3. Minimumvalue components (EQN4)
All three VCO models must cover the desired nominal frequency. Figure 5 shows how the three designs must converge to provide a manufacturable design solution. Observations of EQN1 and
Figure 5 reveal that
minimumvalue components shift the oscillation frequency
higher, and
maximumvalue components shift the oscillation frequency
lower.
Figure 5. Worstcase and nominaltank centering.
Minimum tuning range must be used in order to design a tank with the best closedloop phase noise. Therefore, the nominal tank should be designed to cover the center frequency with overlap to take into account device tolerance. The worstcase hightune tank and worstcase lowtune tank should tune just to the edge of the desired oscillation frequency. EQN2 can be modified by component tolerance to produce a worstcase hightune tank EQN4 and worstcase lowtune tank EQN5.

EQN4


EQN5

T
_{L} = % tolerance of inductor (L)
T
_{CINT} = % tolerance of capacitor (C
_{INT})
T
_{CCENT} = % tolerance of capacitor (C
_{CENT})
T
_{CCOUP} = % tolerance of capacitor (C
_{COUP})
T
_{CV} = % tolerance of varactor capacitance (C
_{V})
EQN4 and EQN5 assume that the strays do not have a tolerance.
General Design Procedure
Step 1
Estimate or measure pad capacitance and other strays. The stray capacitance on the MAX2360 Rev A EV Kit has been measured with a Boonton Model 72BD capacitance meter. C
_{LP} = 0.981pF, C
_{VP} = 0.78pF, C
_{DIFF} = 0.118pF.
Step 2
Determine the value for capacitance C
_{int}. This can be found in the MAX2360/MAX2362/MAX2364 Data Sheet on page 5. The typical operating characteristic TANK 1/S11 vs. FREQUENCY shows the equivalent parallel RC values for several popular LO frequencies. Keep in mind that the LO frequency is twice the IF frequency.
Example:
For an IF frequency of 130MHz, the LO operates at 260MHz. From the 1/s11 chart, R
_{n} = 1.66kΩ and C
_{int} = 0.31pF.
Step 3
Choose an inductor. A good starting point is using the geometric mean. This is an iterative process.

EQN6

This equation assumes L in (nH) and C in (pF) (1x10
^{9} x 1x10
^{12} = 1x10
^{21}). L = 19.3nH for a f
_{osc} = 260.76MHz. This implies a total tank capacitance C = 19.3pF. An appropriate initial choice for an inductor would be 18nH Coilcraft 0603CS18NXGBC 2% tolerance.
When choosing an inductor with finite step sizes, the following formula EQN6.1 is useful. The total product LC should be constant for a fixed oscillation frequency f
_{osc}.

EQN6.1

LC = 372.5 for a f
_{osc} = 260.76MHz. The trialanderror process with the spreadsheet in Table1 yielded an inductor value of 39nH 5% with a total tank capacitance of 9.48pF. The LC product for the tank in
Figure 6 is 369.72, which is close enough to the desired LC product of 372.5. One can see this is a useful relationship to have on hand. For best phase noise, choose a high Q inductor like the Coilcraft 0603CS series. Alternatively, a microstrip inductor can be used if the tolerance and Q can be controlled reasonably.
Figure 6. 130.38MHz IF tank schematic.
Step 4
Determine the PLL compliance range. This is the range the VCO tuning voltage (V
_{tune}) is designed to work over. For the MAX2360, the compliance range is 0.5V to V
_{CC}0.5V. For a V
_{CC} = 2.7V, this would set the compliance range to 0.5 to 2.2V. The chargepump output sets this limit. The voltage swing on the tank is 1V
_{PP} centered at 1.6VDC. Even with large values for C
_{coup}, the varactor diodes are not forwardbiased. This is a condition to be avoided, as the diode rectifies the AC signal on the tank pins, producing undesirable spurious response and loss of lock in a closedloop PLL.
Step 5
Choose a varactor. Look for a varactor with good tolerance over your specified compliance range. Keep the series resistance small. For a figure of merit, check that the selfresonant frequency of the varactor is above the desired operating point. Look at the C
_{V}(2.5V)/C
_{V}(0.5V) ratio at your voltage compliance range. If the coupling capacitors C
_{coup} were chosen large, then the maximum tuning range can be calculated using EQN2. Smaller values of capacitor C
_{coup} reduce this effective frequency tuning range. When choosing a varactor, it should have a tolerance specified at your given compliancerange mid and end points. Select a hyperabrupt varactor such as the Alpha SMV1763079 for the linear tuning range. Take the value for total tank capacitance, and use that for Cjo of the varactor. Remember that C
_{coup} reduces the net capacitance coupled to the tank.
Step 6
Pick a value for C
_{coup}. Large values of C
_{coup} increase the tuning range by coupling more of the varactor in the tank at the expense of decreasing tank loaded Q. Smaller values of C
_{coup} increase the effective Q of the coupled varactor and loaded Q of the tank at the expense of reducing the tuning range. Typically this value is chosen as small as possible, while still getting the desired tuning range. Another benefit of choosing a small value for C
_{coup} is that it reduces the voltage swing across the varactor diode. This helps thwart forwardbiasing the varactor.
Step 7
Pick a value for C
_{cent}, which is usually around 2pF or greater for tolerance purposes. Use C
_{cent} to center up the VCO's frequency.
Step 8
Iterate with the spreadsheet.
MAX2360VCO Tank Designs for IF Frequencies of 130.38MHz, 165MHz, and 380MHz
The following spreadsheets show designs for several popular IF frequencies for the MAX2360. Keep in mind that the LO oscillates at twice the desired IF frequency.

Light grey indicates calculated values 

Darker grey indicates user input 
Table 1. 130.38MHz IF Tank
Design
MAX2360
Tank Design and Tuning Range for 130.38MHz IF Frequency 
Total
Tank Capacitance vs. V tune 
V tune

Total
C 
Ct
(Nominal) 
Ct
(Low) 
Ct
(High) 
0.5V 
Ct
high 
10.9296pF 
10.1242pF 
11.6870pF 
1.375V 
Ct
mid 
9.4815pF 
8.4068pF 
10.4077pF 
2.2V 
Ct
low 
8.0426pF 
6.9014pF 
9.0135pF 

Tank
Components 
Tolerance

C coup

18pF

0.9pF

5%

C cent

2.7pF

0.1pF

4%

C stray

0.69pF



L

39nH

5.00%


C int

0.31pF

10.00%



Parasitics
and Pads (C stray) 
Due to
Q 
C L

0.08pF

Ind. pad 
C Lp

0.981pF

Due to
 
C diff

0.118pF

Var. pad 
C vp

0.78pF


Varactor
Specs 
Alpha
SMV1255003 
Cjo 
82pF

Varactor Tolerance

Vj 
17V

0.5V

19.00%

M 
14

1.5V

29.00%

Cp 
0pF

2.5V

35.00%

Rs 
1Ω

Reactance

Ls 
1.7nH

X Ls

2.79 
Freq 
260.76MHz



Nominal
Varactor 
X
c

Net Cap

Cv high

54.64697pF

11.16897

72.80216pF

Cv mid

27.60043pF

22.11379

31.57772pF

Cv low

14.92387pF

40.89758

16.01453pF


Negative
Tol Varactor (Low Capacitance) 
Cv high

44.26404pF

13.78885

55.46841pF

Cv mid

19.59631pF

31.14619

21.52083pF

Cv low

9.700518pF

62.91935

10.14983pF


Positive
Tol Varactor (High Capacitance) 
Cv high

65.02989pF

9.385688

92.47168pF

Cv mid

35.60456pF

17.14248

42.51182pF

Cv low

20.14723pF

30.2945

22.18712pF



Nominal
LO
(Nom) Range 
Low
Tol IF
(High) Range 
Nominal
IF
(Nom) Range 
High
Tol IF
(Low) Range 
F low

243.77MHz

129.93MHz

121.89MHz

115.03MHz

F mid

261.73MHz

142.59MHz

130.86MHz

121.90MHz

F high

284.18MHz

157.37MHz

142.09MHz

130.98MHz

BW

40.40MHz

27.44MHz

20.20MHz

15.95MHz

% BW

15.44%

19.24%

15.44%

13.09%


Nominal
IF Frequency 
130.38MHz


Design
Constraints

Condition for
bold number 
<IF

=IF

> IF

Delta 
0.45

0.48

0.60

Test 
pass

pass

pass

Raise
or lower cent freq by 
0.48

MHz

Inc or
dec BW 
1.05

MHz

Cent
adj for min BW 
130.46

MHz


K vco 
23.77MHz/V

Figure 7. 165MHz IF tank schematic.

Light grey indicates calculated values 

Darker grey indicates user input 
Table 2. 165MHz
IF Tank Design
MAX2360
Tank Design and Tuning Range for 165MHz IF Frequency 
Total
Tank Capacitance vs. V tune 
V tune

Total
C 
Ct
(Nominal) 
Ct
(Low) 
Ct
(High) 
0.5V

Ct
high 
10.0836pF 
9.2206pF 
10.8998pF 
1.375V

Ct
mid 
8.5232pF 
7.3878pF 
9.5095pF 
2.2V

Ct
low 
7.0001pF 
5.8130pF 
8.0193pF 

Tank
Components 
Tolerance

C coup

18pF

0.9pF

5%

C cent

1.6pF

0.1pF

6%

C stray

0.62pF



L

27nH

5.00%


C int

0.34pF

10.00%



Parasitics
and Pads (C stray) 
Due to Q 
C L

0.011pF

Ind. pad 
C Lp

0.981pF

Due to  
C diff

0.118pF

Var. pad 
C vp

0.78pF


Varactor
Specs 
Alpha
SMV1255003 
Cjo 
82pF

Varactor Tolerance

Vj 
17V

0.5V

19.00%

M 
14

1.5V

29.00%

Cp 
0pF

2.5V

35.00%

Rs 
1ohm

Reactance

Ls 
1.7nH

X Ls

3.52 
Freq 
330.00MHz



Nominal
Varactor 
X c

Net Cap

Cv high

54.646968pF

8.8255163

90.986533pF

Cv mid

27.600432pF

17.473919

34.574946pF

Cv low

14.923873pF

32.316524

16.750953pF


Negative
Tol Varactor (Low Capacitance) 
Cv high

44.264044pF

10.895699

65.431921pF

Cv mid

19.596307pF

24.611153

22.872103pF

Cv low

9.7005176pF

49.717729

10.440741pF


Positive
Tol Varactor (High Capacitance) 
Cv high

65.029892pF

7.4164003

123.93257pF

Cv mid

35.604558pF

13.545673

48.128632pF

Cv low

20.147229pF

23.938166

23.626152pF



Nominal
LO
(Nom) Range 
Low
Tol IF
(High) Range 
Nominal
IF
(Nom) Range 
High
Tol IF
(Low) Range 
F low

305.02MHz

163.63MHz

152.51MHz

143.15MHz

F mid

331.77MHz

182.81MHz

165.88MHz

153.26MHz

F high

366.09MHz

206.08MHz

183.04MHz

166.90MHz

BW

61.07MHz

42.45MHz

30.53MHz

23.74MHz

% BW

18.41%

23.22%

18.41%

15.49%


Nominal
IF Frequency 
165MHz


Design
Constraints

Condition for
bold number 
< IF

= IF

> IF

Delta 
1.37

0.88

1.90

Test 
pass

pass

pass

Raise or lower cent freq
by 
0.88

MHz

Inc or dec BW 
3.26

MHz

Cent adj for min BW 
165.26

MHz


K vco 
35.92MHz/V

Figure 8. 380MHz IF tank schematic.

Light grey indicates calculated values 

Darker grey indicates user input 
Table 3. 380MHz IF Tank
Design
MAX2360
Tank Design and Tuning Range for 380MHz IF Frequency 
Total
Tank Capacitance vs. V tune 
V tune

Total C 
Ct
(Nominal) 
Ct
(Low) 
Ct (High) 
0.5V

Ct high 
6.9389pF 
6.6119pF 
7.2679pF 
1.35V

Ct mid 
6.2439pF 
5.9440pF 
6.5449pF 
2.2V

Ct low 
5.7813pF 
5.5040pF 
6.0593pF 

Tank
Components 
Tolerance

C coup

15pF

0.8pF

5%

C cent

2.4pF

0.1pF

4%

C stray

1.42pF



L

6.8nH

2.00%


C int

0.43pF

10.00%



Parasitics
and Pads (C stray) 
Due to Q 
C L

0.08pF

Ind. pad 
C Lp

0.981pF

Due to  
C diff

0.85pF

Var. pad 
C vp

0.78pF


Varactor
Specs 
Alpha SMV1255003 
Cjo 
8.2pF

Varactor Tolerance

Vj 
15V

0.5V

7.50%

M 
9.5

1.5V

9.50%

Cp 
0.67pF

2.5V

11.50%

Rs 
0.5Ω

Reactance

Ls 
0.8nH

X Ls

3.82 
Freq 
760.00MHz



Nominal
Varactor 
X
c

Net
Cap

C_{V} high

6.67523pF

31.37186

7.600784pF

C_{V} mid

4.286281pF

48.8569

4.649858pF

C_{V} low

2.904398pF

72.10251

3.06689pF


Negative
Tol Varactor (Low Capacitance) 
C_{V} high

6.174588pF

33.91552

6.958364pF

C_{V} mid

3.879084pF

53.98553

4.174483pF

C_{V} low

2.570392pF

81.47176

2.696846pF


Positive
Tol Varactor (High Capacitance) 
C_{V} high

7.175873pF

29.18313

8.256705pF

C_{V} mid

4.693477pF

44.61818

5.132957pF

C_{V} low

3.238404pF

64.66593

3.441726pF



Nominal
LO
(Nom) Range 
Low
Tol IF
(High) Range 
Nominal
IF
(Nom) Range 
High
Tol IF
(Low) Range 
F low

732.69MHz

379.11MHz

366.35MHz

354.43MHz

F mid

772.40MHz

399.84MHz

386.20MHz

373.50MHz

F high

802.70MHz

415.51MHz

401.35MHz

388.17MHz

BW

70.00MHz

36.41MHz

35.00MHz

33.74MHz

% BW

9.06%

9.11%

9.06%

9.03%


Nominal IF Frequency 
380MHz


Design
Constraints

Condition for
bold number 
< IF

= IF

> IF

Delta 
0.89

6.20

8.17

Test 
pass

pass

pass

Raise or lower cent freq
by 
6.20

MHz

Inc or dec BW 
9.07

MHz

Cent adj for min BW 
383.64

MHz


K vco 
41.18MHz/V

Appendix A
Figure 9. Varactor model.
Alpha Application Note AN1004 has additional information on varactor models. Varactor capacitance is defined in EQN7.

EQN7

Alpha SMV1255003 
Alpha SMV1763079 
C_{jo} = 82 pF 
C_{jo} = 8.2 pF 
V_{j} =17 V 
V_{j} =15 V 
M = 14 
M = 9.5 
C_{p} = 0 
C_{p} = 0.67 
R_{s} = 1Ω 
R_{s} = 0.5Ω 
L_{s} = 1.7 nH 
L_{s} = 0.8 nH 
The series inductance of the varactor is taken into account by backing
out the inductive reactance and calculating a new effective capacitance
C
_{V}.

EQN8

References
 Chris O'Connor, Develop Trimless VoltageControlled Oscillators, Microwaves and RF, July 1999.
 Wes Hayward, Radio Frequency Design, Chapter 7.
 Krauss, Bostian, Raab, Solid State Radio Engineering, Chapters 2, 3, 5.
 Alpha Industries Application Note AN1004.
 Coilcraft, RF Inductors Catalog, March 1998, p.131.
 Maxim, MAX2360/MAX2362/MAX2364 Data Sheet Rev 0.
 Maxim, MAX2360 Evaluation Kit Data Sheet Rev 0.