Abstract
This application note presents various voltagecontrolled oscillator (VCO) designs for popular IF frequencies of 85MHz, 190MHz, and 210MHz. These designs reduce the number of iterations required for optimized results. Analysis can be accomplished with a simple spreadsheet program.
Additional Information:
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Introduction
This application note presents various voltagecontrolled oscillator (VCO) designs for popular IF frequencies of 85MHz, 190MHz, and 210MHz. 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 MAX2310 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 MAX2310 tank port
C_{t} = total equivalent capacitance of the tank circuit
Figure 1. Basic VCO model.
R_{n} = equivalent negative resistance of the MAX2310 tank port
C_{int} = internal capacitance of the MAX2310 tank port
C_{t} = total equivalent capacitance of the tank circuit
L = inductance of the coil in the tank circuit
Figure 2. The MAX2310 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 oscillation frequency to a nominal value. It is not required but adds a degree of freedom by allowing one 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 loadedtank 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 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 MAX2310 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} = varactorpad 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 the inductor pads
C_{DIFF} = capacitance due to parallel traces
Figure 4. Detailed VCO model.
R_{n} = equivalent negative resistance of the MAX2310 tank port
C_{int} = internal capacitance of the MAX2310 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} = varactorpad capacitance
L_{S} = series inductance of the varactor
R = resistance of the 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 MAX2310 is 0.5V to Vcc0.5V. In batterypowered applications, the compliance range is usually fixed by battery voltage or a regulator.
Basic Concept for Trimless Design
VCO design for 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 the 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 possible tuning gain, and the lower the closedloop phase noise. For worstcase error budget design, we will look at three VCO models:
 Maximumvalue components (EQN5)
 Nominal tank, all components perfect (EQN2)
 Minimumvalue components (EQN4)
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 a worstcase lowtune tank EQN5.
EQN4

EQN5

T_{L} = % tolerance of the inductor (L)
T_{CINT} = % tolerance of the capacitor (C_{INT})
T_{CCENT} = % tolerance of the capacitor (C_{CENT})
T_{CCOUP} = % tolerance of the capacitor (C_{COUP})
T_{CV} = % tolerance of the 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 MAX2310 Rev C EV kit has been measured with a Boonton Model 72BD capacitance meter. C_{LP} = 1.13pF, C_{VP} = 0.82pF, C_{DIFF} = 0.036pF.
Step 2
Determine the value for capacitance C_{int}. This can be found in the MAX2310/MAX2312/MAX2314/MAX2316 data sheet on Page 5. Typical operating characteristic TANKH PORT 1/S11 vs. FREQUENCY shows the equivalent parallel RC values for several popular LO frequencies. Appendix B includes tables of C_{int} versus frequency for the high and lowband tank ports. Keep in mind that the LO frequency is twice the IF frequency.
Example:
For an IF frequency of 210MHz (highband tank), the LO will operate at 420MHz. From Appendix B, Table 5, C_{int} = 0.959pF.
Step 3
Choose an inductor. A good starting point is using the geometric mean. This will be an iterative process.
EQN6

This equation assumes L in (nH) and C in (pF) (1x10^{9} x 1x10^{12} = 1x10^{21}). L = 11.98nH for a f_{osc} = 420MHz. This implies a total tank capacitance C = 11.98pF. An appropriate initial choice for an inductor would be 12nH Coilcraft 0805CS12NXGBC 2% tolerance.
When choosing an inductor with finite step sizes, the following formula EQN6.1 will be useful. The total product LC should be constant for a fixed oscillation frequency f_{osc}.
EQN6.1

LC = 143.5 for a f_{osc} = 420MHz. The trialanderror process with the spreadsheet in Table 3 yielded an inductor value of 18nH 2% with a total tank capacitance of 7.9221pF. The LC product for the tank in Figure 8 is 142.59, close enough to the desired LC product of 143.5. One can see this is a useful relationship to have on hand. For best phase noise, choose a highQ inductor like the Coilcraft 0805CS series. Alternatively, a microstrip inductor can be used if the tolerance and Q can be controlled reasonably.
Step 4
Determine the PLL compliance range. This is the range over which the VCO tuning voltage (V_{tune}) will be designed to work. For the MAX2310, the compliance range is 0.5V to Vcc0.5V. For a Vcc = 2.7V, this would set the compliance range to 0.5 to 2.2V. The chargepump output will set this limit. The voltage swing on the tank is 1Vpp centered at 1.6VDC. Even with large values for C_{coup}, the varactor diodes will not be forwardbiased. This is a condition to be avoided, as the diode will rectify 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 compliancerange voltage. 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} will 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 linear tuning response. Take the value for total tank capacitance, and use that for Cjo of the varactor. Remember, C_{coup} will reduce the net capacitance coupled to the tank.
Step 6
Pick a value for C_{coup}. Large values of C_{coup} will increase tuning range by coupling more of the varactor into the tank at the expense of decreasing tankloaded Q. Smaller values of C_{coup} will increase the effective Q of the coupled varactor and loaded Q of the tank at the expense of reducing tuning range. Typically this will be chosen as small as possible, while still getting the desired tuning range. Another benefit of choosing C_{coup} small is that it reduces the voltage swing across the varactor diode. This will help thwart forwardbiasing the varactor.
Step 7
Pick a value for C_{cent}, usually around 2pF or greater for tolerance purposes. Use C_{cent} to center the VCO's nominal frequency.
Step 8
Iterate with the spreadsheet.
MAX2310 VCO Tank Designs for IF Frequencies of 85MHz, 190MHz, and 210MHz
The following spreadsheets show designs for several popular IF frequencies for the MAX2310. Keep in mind that the LO oscillates at twice the desired IF frequency.
Figure 6. 85MHz lowband IF tank schematic.
Table 1. 85MHz LowBand IF Tank Design
Light grey indicates calculated values. 
Darker grey indicates user input. 
MAX2310 LowBand Tank Design and Tuning Range  
Total Tank Capacitance vs. V tune  
V tune  Total C  Ct
(Nominal) 
Ct (Low) 
Ct (High) 

0.5V  Ct high  14.1766pF  13.3590pF  14.9459pF  
1.375V  Ct mid  12.8267pF  11.7445pF  13.7620pF  
2.2V  Ct low  11.4646pF  10.3049pF  12.4534pF  
Tank Components 


C coup

18pF

0.9pF

5%


C cent

5.6pF

0.1pF

2%


C stray

0.70pF


L

68nH

2.00%


C int

0.902pF

10.00%


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

0.1pF


Ind. pad 
C Lp

1.13pF


Due to  
C diff

0.036pF


Var. pad 
C vp

0.82pF


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

1.82  
Freq 
170.00MHz


Nominal Varactor 
X c

Net Cap


Cv high

54.64697pF

17.1319

61.12581pF


Cv mid

27.60043pF

33.92

29.16154pF


Cv low

14.92387pF

62.7321

15.36874pF


Negative Tol Varactor (Low Capacitance)  
Cv high

44.26404pF

21.1505

48.42117pF


Cv mid

19.59631pF

47.7746

20.37056pF


Cv low

9.700518pF

96.5109

9.886531pF


Positive Tol Varactor (High Capacitance)  
Cv high

65.02989pF

14.3965

74.41601pF


Cv mid

35.60456pF

26.2945

38.24572pF


Cv low

20.14723pF

46.4682

20.96654pF


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

F low

162.10MHz

84.34MHz

81.05MHz

78.16MHz


F mid

170.42MHz

89.95MHz

85.21MHz

81.45MHz


F high

180.25MHz

96.03MHz

90.13MHz

85.62MHz


BW

18.16MHz

11.69MHz

9.08MHz

7.46MHz


% BW

10.65%

12.99%

10.65%

9.16%


Nominal IF Frequency 


Design
Constraints


Condition for bold number 
<IF

=IF

> IF


Delta 
0.66

0.21

0.62


Test 
pass

pass

pass


Raise or lower cent freq by 
0.21

MHz


Inc or dec BW 
1.28

MHz


Cent adj for min BW 
84.98

MHz


K vco 
10.68MHz/V

Figure 7. 190MHz highband IF tank schematic.
Table 2. 190MHz HighBand IF Tank Design
Light grey indicates calculated values. 
Darker grey indicates user input. 
MAX2310 HighBand Tank Design and Tuning Range  
Total Tank Capacitance vs. V tune  
V tune

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

0.5V

Ct high  10.4968pF  10.0249pF  10.9126pF  
1.375V

Ct mid  9.6292pF  8.8913pF  10.2124pF  
2.2V

Ct low  8.6762pF  7.7872pF  9.3717pF  
Tank Components 


C coup

12pF

0.1pF

1%


C cent

3.4pF

0.1pF

3%


C stray

0.70pF


L

18nH

2.00%


C int

0.954pF

10.00%


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

0.01pF


Ind. pad 
C Lp

1.13pF


Due to  

0.036pF


Var. pad 
C vp

0.82pF


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

4.06  
Freq 
380.00MHz


Nominal Varactor 
X c

Net Cap


Cv high

54.64697pF

7.66426

116.1695pF


Cv mid

27.60043pF

15.1747

37.67876pF


Cv low

14.92387pF

28.0643

17.44727pF


Negative Tol Varactor (Low Capacitance)  
Cv high

44.26404pF

9.46205

77.51615pF


Cv mid

19.59631pF

21.3728

24.19031pF


Cv low

9.700518pF

43.1759

10.70708pF


Positive Tol Varactor (High Capacitance)  
Cv high

65.02989pF

6.44056

175.8588pF


Cv mid

35.60456pF

11.7633

54.36221pF


Cv low

20.14723pF

20.7884

25.03539pF


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

F low

366.15MHz

189.23MHz

183.07MHz

177.78MHz


F mid

382.29MHz

200.94MHz

191.14MHz

183.78MHz


F high

402.74MHz

214.71MHz

201.37MHz

191.84MHz


BW

36.59MHz

25.47MHz

18.29MHz

14.06MHz


% BW

9.57%

12.68%

9.57%

7.65%


Nominal IF Frequency 


Design
Constraints


Condition for bold number 
< IF

= IF

> IF


Delta 
0.77

1.14

1.84


Test 
pass

pass

pass


Raise or lower cent freq by 
1.14

MHz


Inc or dec BW 
2.61

MHz


Cent adj for min BW 
190.54

MHz


K vco 
21.52MHz/V

Figure 8. 210MHz highband IF tank schematic.
Table 3. 210MHz HighBand IF Tank Design
Light grey indicates calculated values. 
Darker grey indicates user input. 
MAX2310 HighBand Tank Design and Tuning Range  
Total Tank Capacitance vs. V tune  
V tune

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

Ct high  8.8304pF  8.1465pF  9.4877pF  
1.35V

Ct mid  7.9221pF  7.0421pF  8.6970pF  
2.2V

Ct low  6.9334pF  5.9607pF  7.7653pF  
Tank Components 


C coup

12pF

0.6pF

5%


C cent

1.6pF

0.1pF

6%


C stray

0.70pF


L

18nH

2.00%


C int

0.959pF

10.00%


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

0.1pF


Ind. pad 
C Lp

1.13pF


Due to  
C diff

0.036pF


Var. pad 
C vp

0.82pF


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

4.49  
Freq 
420.00MHz


Nominal Varactor 
X
c

Net
Cap


Cv high

54.64697pF

6.93433

154.787pF


Cv mid

27.60043pF

13.7295

40.99616pF


Cv low

14.92387pF

25.3916

18.12647pF


Negative Tol Varactor (Low Capacitance)  
Cv high

44.26404pF

8.56091

92.99806pF


Cv mid

19.59631pF

19.3373

25.51591pF


Cv low

9.700518pF

39.0639

10.95908pF


Positive Tol Varactor (High Capacitance)  
Cv high

65.02989pF

5.82717

282.5852pF


Cv mid

35.60456pF

10.643

61.54791pF


Cv low

20.14723pF

18.8086

26.45795pF


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

F low

399.20MHz

209.92MHz

199.60MHz

190.67MHz


F mid

421.47MHz

225.78MHz

210.73MHz

199.14MHz


F high

450.52MHz

245.41MHz

225.26MHz

210.75MHz


BW

51.31MHz

35.49MHz

25.66MHz

20.09MHz


% BW

12.18%

15.72%

12.18%

10.09%


Nominal IF Frequency 


Design
Constraints


condition for bold number 
< IF

= IF

> IF


Delta 
0.08

0.73

0.75


Test 
pass

pass

pass


Raise or lower cent freq by 
0.73

MHz


Inc or dec BW 
0.83

MHz


Cent adj for min BW 
210.34

MHz


K vco 
30.18MHz/V

Figure 9. HighQ 210MHz highband IF tank schematic.
Table 4. HighQ 210MHz HighBand IF Tank Design
Light grey indicates calculated values. 
Darker grey indicates user input. 
MAX2310 HighBand Tank Design and Tuning Range  
Total Tank Capacitance vs. V tune  
V tune

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

Ct high  5.8856  5.5289  6.2425  
1.375V

Ct mid  5.2487  4.9113  5.5858  
2.2V

Ct low  4.8371  4.5156  5.1581  
Tank Components


C coup

15pF

0.75pF

5%


C cent

1.6pF

0.1pF

6%


C stray

0.77pF


L

27

2.00%


C int

0.959

10.00%


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

0.17pF


Ind. pad 
C Lp

1.13pF


Due to  
C diff

0.036pF


Var. pad 
C vp

0.82pF


Varactor Specs  
Alpha SMV1763079  
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

2.11  
Freq 
420.00MHz


Nominal Varactor 
X
c

Net
Cap


Cv high

6.67523pF

56.7681

6.933064pF


Cv mid

4.23417pF

89.4958

4.336464pF


Cv low

2.904398pF

130.471

2.952167pF


Negative Tol Varactor (Low Capacitance)  
Cv high

6.174588pF

61.3709

6.39456pF


Cv mid

3.831924pF

98.8904

3.915514pF


Cv low

2.570392pF

147.425

2.607736pF


Positive Tol Varactor (High Capacitance)  
Cv high

7.175873pF

52.8076

7.474698pF


Cv mid

4.636416pF

81.7313

4.759352pF


Cv low

3.238404pF

117.015

3.297904pF


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

F low

399.25MHz

208.05MHz

199.62MHz

191.92MHz


F mid

422.78MHz

220.75MHz

211.39MHz

202.89MHz


F high

440.40MHz

230.22MHz

220.20MHz

211.14MHz


BW

41.15MHz

22.16MHz

20.58MHz

19.21MHz


% BW

9.73%

10.04%

9.73%

9.47%


Nominal IF Frequency 


Design
Constraints


Condition for bold number 
< IF

= IF

> IF


Delta 
1.95

1.39

1.14


Test 
pass

pass

pass


Raise or lower cent freq by 
1.39

MHz


Inc or dec BW 
3.08

MHz


Cent adj for min BW 
209.60

MHz


K vco 
24.21MHz/V

Appendix A
Figure 10. 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

Appendix B
Table 5. C_{int} vs. Frequency for the MAX2310 HighBand Tank
Frequency (MHz)  C_{int} (pF)  Frequency (MHz) (cont.)  C_{int} (pF) (cont.) 
100  0.708  360  0.949 
110  0.759  370  0.955 
120  0.800  380  0.954 
130  0.809  390  0.954 
140  0.839  400  0.954 
150  0.822  410  0.955 
160  0.860  420  0.959 
170  0.869  430  0.956 
180  0.880  440  0.959 
190  0.905  450  0.964 
200  0.917  460  0.962 
210  0.920  470  0.963 
220  0.926  480  0.963 
230  0.924  490  0.960 
240  0.928  500  0.964 
250  0.935  510  0.965 
260  0.932  520  0.968 
270  0.931  530  0.966 
280  0.933  540  0.968 
290  0.927  550  0.967 
300  0.930  560  0.974 
310  0.933  570  0.977 
320  0.943  580  0.976 
330  0.944  590  0.984 
340  0.945  600  0.982 
350  0.956     
Figure 11. C_{int} vs. frequency for the MAX2310 highband tank (sixthorder polynomial curve fit)
Table 6. C_{int} vs. Frequency for the MAX2310 LowBand Tank
Frequency (MHz)  C_{int} (pF)  Frequency (MHz) (cont.)  C_{int} (pF) (cont.) 
100  0.550  360  1.001 
110  0.649  370  0.982 
120  0.701  380  0.992 
130  0.764  390  1.001 
140  0.762  400  0.985 
150  0.851  410  0.980 
160  0.838  420  0.986 
170  0.902  430  0.992 
180  0.876  440  0.994 
190  0.907  450  1.001 
200  0.913  460  1.003 
210  0.919  470  1.007 
220  0.945  480  0.992 
230  0.952  490  1.010 
240  0.965  500  1.004 
250  0.951  510  1.011 
260  0.954  520  1.022 
270  0.974  530  1.019 
280  0.980  540  1.044 
290  0.973  550  1.026 
300  0.982  560  1.041 
310  0.970  570  1.038 
320  0.982  580  1.032 
330  0.991  590  1.036 
340  0.993  600  1.025 
350  0.991     
Figure 12. C_{int} vs. frequency for the MAX2310 lowband tank (sixthorder polynomial curve fit).
References
 Chris O'Connor, Develop Trimless VoltageControlled Oscillators, Microwaves and RF, July1999.
 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, MAX2310/MAX2312/MAX2314/MAX2316 Data Sheet, Rev 0.
 Maxim, MAX2310/MAX2314 Evaluation Kit Data Sheet, Rev 0.
 Maxim, MAX2312/MAX2316 Evaluation Kit Data Sheet, Rev 0.