Project Design Goals 1 To design and construct a small size multi band transmitting loop antenna useful for QRP and portable operation 2 To compare the performance of the loop ID: 675653
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Slide1
Small Magnetic Loop Antenna Design
Project Design
Goals
:
1. To design and construct
a small size, multi- band transmitting
loop
antenna useful for QRP and portable operation.
2. To compare the performance of the loop
antenna
to
a known antenna type to verify performance
3. Design will cover the 40 through 15 Meter Bands inclusively
4.
To develop a computer spreadsheet to
facilitate
the
design procedure Slide2
First Generation 30 inch LoopSlide3
First Generation Design
30 inch loop using Gamma MatchSlide4
Original design used a 30 inch loop which did not tune below 14 MHz, and had efficiency issues because of the 30 inch diameter and conductor diameter (0.65 inches)The gamma match produced a current imbalance in the loop (“antenna effect”), which distorted the radiation pattern
First Generation ShortcomingsSlide5
Remote tuning
At least 30 w
power handling
capability
Portable for Field use
Cost of materials not to exceed $100.00
VSWR
less than 1.5 to 1 on all covered bands at resonance
Specific
Design
Goals Slide6
1
inch copper tubing
was investigated at first, but was dismissed because of cost and weight
.
D
esign analysis
indicated that a 42 inch diameter loop would provide a good compromise between array efficiency and frequency coverage. (ARRL Antenna Book, Antennas, by John Kraus)) A plastic gymnasium hoop
had approximately the right diameter, is low cost and light in weight
Could copper tape be used as the radiating conductor? Skin depth will have to be considered as one of the design tasks.
Selection
of materialsSlide7
6. For remote tuning, a low cost 12 volt hobby motor was selected at 0.7 RPM.
Motor
rotates in both directions
7.
The loop will use a single
coax lead-in to the
antenna
, therefore a suitable power insertion system will be designed to feed the DC control voltage up the center conductor, along with the RF signal. A control
box
with reversing polarity control voltage will be part of the design. 8. Determine the type and range of the tuning capacitor to resonate the loop
Selection of materials (continued)Slide8
1. Small loop:
A completely encircled antenna structure whose total
perimeter is below self-resonance
2. Directivity (Gain):
The ratio of loop Field Strength (in the favored direction) compared to the Field Strength of an Isotropic Radiator (or dipole)
3. Loop Efficiency (Decimal or Percent):
The ratio of Loop Radiation Resistance divided by the Sum of Radiation Resistance plus Total Loss
Resistance (Decimal). For percent, multiply decimal
value
by 100.
4. Skin Depth (Skin Effect): The distance from the top of a conducting medium where the current density decreases to 1/є of its surface value (37%) Skin Depth is denoted as δ; 86% of the total current density is contained within 2δ.
Definitions
:Slide9
Skin Depth Equation for pure copper conductor:
δ
≈
0.002574
√ F
Where:
δ
is the skin depth in inches, and F is the Frequency in MHz
At
7 MHz, δ ≈ 0.973 x 10-3 inches 2 x
δ
=
1.95
x 10-3 inches and, At 21 MHz, δ ≈ 0.515 x 10-3 inches 2 x δ = 1.03 x 10-3 inches Calculation of Skin Depth:Slide10
Worst
case is
7 MHz,
requiring the greatest RF
current
penetration
.
Since 1 mil = 10
-3 inches, at 7 MHz, a minimum conductor thickness of 1.95 mils is required for at
least
2δ depth of current density penetration.
3M Copper
Adhesive Tape
has a conductor thickness of 2 mils, which satisfies the requirement, and was chosen for the radiating conductor. Slide11
Loop Design Procedure for Circular Loop:
1.
Choose
loop diameter,
D
, and radiator diameter,
d
, both in inches. D must be
less than
≈
3300 where f
is the highest frequency of the loop
П f in MHZ. At 21 MHz, D must be less than 50 inches. 42 inches was chosen for this design, with radiator diameter of 1.5 inches
2. Calculate
the Loop Inductance, L
:
L
(
μ
H) = 0.005 D
x
{ [ 7.353
x
( LOG ( 8
x
D / d )] – 6.386 }
Slide12
3. Calculate the Loop Inductive Reactance, X
L,
at the highest and lowest antenna frequencies
:
X
L
= 2 x П x F x L
where:X
L
is Inductive Reactance in ohms
F is the Frequency in MHZ (highest / lowest), and L is the Loop Inductance in μH calculated in Step 2
4. Calculate the distributed loop Self Capacitance, C
S
:
C
S (pf) ≈ 0.2103 x D, with D again in inches 5. Calculate the required Capacitances to Resonate the Loop, C min and C max: C min = 106 / ( 2 x П x Fmax x XLH ) - CS, and C max = 106 / ( 2 x П x Fmin x XLL ) - CS, where: C min and C max are in pico-farads, Fmin / Fmax in MHZ XLH is the inductive reactance at the highest frequency XLL is the inductive reactance at the lowest frequency
Slide13
6. Estimate Tuning capacitor
Qc,
or use published
/ measured capacitor Qc
data. For estimate,
use
2000
to
800 for standard variable capacitor, (fully meshed to unmeshed);
and
3500 to 1000 for split rotor Butterfly
type, (fully meshed to unmeshed
). Refer to spreadsheet
Steps 7 through 17 should be performed at
the highest and lowest antenna frequencies. For these steps, XL is the inductive reactance at the associated frequency.
7
. Calculate capacitor equivalent loss resistance, R
C,
from Q
C
:
RC = XL / QC8. Calculate Loop Radiator Loss Resistance, RL: RL = ( П x D x 0.000083 x √ F ) / d, where D, d, and F are as previously defined9. Total Loss Resistance, RT, is sum of RC + RL RT = RC + RL 10. Calculate Loop Radiation Resistance, RR: RR = 9.926 x 10 -13 x F4
x
D
4
again
, where, F is in MHZ, and D as previously
definedSlide14
1
1
. Calculate antenna efficiency,
ζ
, in percent: *
ζ = {RR / (RT + RR )} x 100,
ζ
D =
ζ
/ 100, which is efficiency expressed as a decimal 12. Calculate the total Loop Antenna Q: * Q = XL / (2x( (RR + RT)) where:
XL is the Loop Inductive Reactance, and RT is the total
Loop
Loss Resistance
,
RR is radiation resistance all as previously
calculated
13. Calculate the Peak Voltage across the tuning Capacitor, VC: * VC = √ (P x XL x Q) where: P is the Peak Envelope Power driving the Loop, XL calculated from Step 3 * 14. Calculate the minimum plate spacing (inches) for the capacitor, SMin: SMin = 1.5 x VC / 50000 (Includes 1.5 to 1 safety factor at 50000 volts / in) * Choose a capacitor offering Cmin and Cmax values (Step 4), with this minimum plate spacing 15. Calculate the RMS Resonant Circulating Current in the Loop, IL: * IL ≈ 0.7071 * VC / XL, provided that XL >> RT, which is the usual case
16: Calculate Loop Bandwidth, BW
: *
BW = F / Q, where F and BW are both in MHZ. * Steps 11 through 16 are within ≈ +/- 20% if Antenna VSWR is better than 1.5 at resonance. Slide15
G dB
≈ 10
x LOG
(
ζ
D
) + 1.81
where:
G dB is the estimated free-space gain in dB
, referenced
to
an
isotropic radiator, and ζ D is the decimal value of the antenna efficiency calculated in STEP 11. 17
. Antenna Gain Estimate:Slide16
Spreadsheet permits Fast Design on Personal Computer by automating
the design steps
.
Calculates all loop parameters
except
the design of the matching / coupling network, which is determined experimentally.
Spreadsheet values are not displayed if loop size exceeds small loop criteria
Computer Aided Design by Spreadsheet:Slide17
From the Spreadsheet, the following values of Rp (Equivalent parallel resistance), are noted for a 42 inch diameter loop:
7 MHz R
P
=
62.88 K
ohms
18 MHz RP = 50.34 K ohms
21 MHz
R
P = 39.73 K ohms These values are calculated from network theory using the series to parallel transform theorem. Rp = Rs + Xs 2 / Rs Xp = Rp Rs / Xs where: Rs = Rc + Ra + Rr Xs = Loop Inductive Reactance , XL, calculated in Step 3
Can
a single matching circuit be used on all bands?
Matching Network Design:Slide18
Loop Series to Parallel
Transformation (Antenna side of Network, using Transformer Coupling)
LA
CA
LA
CASlide19
VSWR on 7 MHz:
VSWR
7
MHz
= R
P
7
MHz / R
P
18 MHz
=
62.88 / 50.34 = 1.25 VSWR on 21 MHz: VSWR 21 MHz = RP
18 MHz
/
R
p 21
MHz = 50.34 / 39.73 = 1.27 From above data, a single coupling loop match of proper spacing would meet the design goal of VSWR less than 1.5 on all bands Design a matching circuit to be close to a perfect match at ≈ 18 MHz, calculate the expected VSWR on the band edges.Slide20
Realization of
Transformer
Match
Secondary coupling loop approx 1/5 diameter of main loop, distance determined experimentallySlide21
Transformer match detailSlide22
Loop after construction and Initial Tests:Slide23
Photo
of
Tuning Unit:Slide24Slide25
Tuning Unit Schematic DiagramSlide26
Control Box Photograph:Slide27Slide28
VSWR (measured using MFJ-469 Analyzer
):
7 MHz
1.2
10 MHz 1.3
14 MHz
1.3 18 MHz
1.1
21 MHz
1.3 7 – 21 MHz Met the design goal of VSWR < 1.5 Tuning Time: Approximately 35 seconds 7 MHz to 21 MHz
Qualitative Gain (switching back-and-forth compared
to ground mounted vertical (one
hop
propagation )
7 MHz
vertical better by approximately 1 S Unit 10 MHz vertical better by approximately ½ S Unit 14 MHz no discernible difference 18 MHz approximately ½ S Unit better on loop 21 MHz approximately ½ S Unit better on loopAntenna was mounted in vertical orientationPower Capability: Tuning Capacitor warm to the touch at 30 watts when keyed for 30 seconds on 7, 10, and 14 MHz bands. Antenna slightly warm on 7 MHz band. No evidence of arcing on any band at 30 watts. Very little capacitor temperature rise noted on 18 and 21 MHz bands. Antenna, itself did not show any rise in temperature on bands above 7 MHz. Measured Performance:Slide29
2.6 to 1 VSWR Bandwidth:
Measured Spreadsheet
7 MHz
approximately
12 KHz 11.2 KHz
10 MHz approximately 20 KHz 19.9 KHz
14 MHz approximately
46 KHz 43.2 KHz
18 MHz approximately 96 KHz 92.5 KHz
21 MHz
approximately
170 KHz 159.6 KHz Measurements are in close agreement with the Spreadsheet.Measured Performance (Continued):Slide30
Item Qty Unit Price Ext
Control Box Plastic enclosure 1 3.50 3.50
Antenna Tuning enclosure 1 6.50 6.50
Hobby motor
0.7
rpm
1
5
.50
5.50Variable
Capacitor (20 -360 pf)
1 20.50 20.50SO-239 connectors 3 3.00 9.00.875 in OD Type 43 Ferrite 3 2.00 6.00Tantalum Capacitors 2 2.00 4.00Disc Capacitors 10 .25 2.5010 volt regulator (LM-7810) 1 1.50 1.501N4007 Diode 2 .25 .5042 in Snap Together Hoop (Amazon) 1
9
.00
9
.00
Dip mica capacitors 3 .50 1.50
Vector Board 1
.50 .50DPDT Momentary Switch 1 2.50 2.502 pin Power connector with mate 3 2.50 2.00Miscellaneous wire and hardware A/R 2.00 (est) 2.00Copper Tape (average 1 roll) A/R 12.00 (est) 12.00 Total $89.50 Priced Bill of Materials:Slide31
1. Design
goal was achieved, to construct a low cost,
small size
loop antenna.
2. VSWR was less than 1.5 on all bands using a single
Coupling Loop
Match section
3.
Qualitative Gain performance was within 1 S Unit of ground mounted vertical mono-pole on 7 and 10 MHz, equal or better on higher bands .
4. Power
handling up to 30 watts PEP.5. Priced Bill of
materials less
than the design goal budget of $100.00
6. Could be an attractive antenna for portable use, or by an amateur who does not have the space for a full sized outdoor antenna
7. Spreadsheet is available via email (Excel) Any Questions? Thank you and See you all on the air 73 de WY2U
Mike Kozma dmkozma@optonline.net
Summary
: