This application note presents three voltage-controlled 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.
This application note presents three voltage-controlled 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:
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
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
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 fine-tune resonance between inductor values. Resistors (R) provide reverse-bias 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 reverse-bias voltage (see Appendix A for the varactor model). V_{tune} is the tuning voltage from a phase-locked 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:
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 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:
C_{L} = capacitance of the inductor
C_{LP} = capacitance of inductor pads
C_{DIFF} = capacitance due to parallel traces
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 reverse-bias 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 closed-loop 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 Vcc-0.5V. In battery-powered applications, the compliance range is usually fixed by the battery voltage or regulator.
Basic Concept for Trimless Design
VCO design manufacturability with real-world 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 closed-loop phase noise. For the worst-case error budget design, we will look at three VCO models:
Maximum-value components (EQN5)
Nominal tank, all components perfect (EQN2)
Minimum-value 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 minimum-value components shift the oscillation frequency higher, and maximum-value components shift the oscillation frequency lower.
Minimum tuning range must be used in order to design a tank with the best closed-loop phase noise. Therefore, the nominal tank should be designed to cover the center frequency with overlap to take into account device tolerance. The worst-case high-tune tank and worst-case low-tune tank should tune just to the edge of the desired oscillation frequency. EQN2 can be modified by component tolerance to produce a worst-case high-tune tank EQN4 and worst-case low-tune tank 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.
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 0603CS-18NXGBC 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}.
LC = 372.5 for a f_{osc} = 260.76MHz. The trial-and-error 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.
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 charge-pump output sets this limit. The voltage swing on the tank is 1V_{P-P} centered at 1.6VDC. Even with large values for C_{coup}, the varactor diodes are not forward-biased. 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 closed-loop 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 self-resonant 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 compliance-range mid and end points. Select a hyperabrupt varactor such as the Alpha SMV1763-079 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 forward-biasing 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 SMV1255-003
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
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
18C vppF
0.78pF
Varactor Specs
Alpha SMV1255-003
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
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
12310.00
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 SMV1255-003
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
Cv high
6.67523pF
-31.37186
7.600784pF
Cv mid
4.286281pF
-48.8569
4.649858pF
Cv low
2.904398pF
-72.10251
3.06689pF
Negative Tol Varactor (Low Capacitance)
Cv high
6.174588pF
-33.91552
6.958364pF
Cv mid
3.879084pF
-53.98553
4.174483pF
Cv low
2.570392pF
-81.47176
2.696846pF
Positive Tol Varactor (High Capacitance)
Cv high
7.175873pF
-29.18313
8.256705pF
Cv mid
4.693477pF
-44.61818
5.132957pF
Cv 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
Alpha Application Note AN1004 has additional information on varactor models. Varactor capacitance is defined in EQN7.
Alpha SMV1255-003
Alpha SMV1763-079
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}.