The Design Concept of K-band Frequency Tripler
Martyna Skweres
Microwave Active Components and EMC Group
PIT-RADWAR S.A.
Warsaw, Poland
martyna.skweres@pitradwar.com
Abstract— In this paper the working principle and fundamental
properties of frequency multipliers are described. The article
presents the frequency tripler solution which generates microwave
signal response in the 18 GHz band (K-band). The various stages
of the designed tripler for the C-band input signal are introduced.
Test results including the third harmonic frequency response of
the manufactured tripler model are also presented.
Assuming that the input voltage is a cosinusoidal signal it is
easy to predict that the higher order harmonics will be received
from the multiplier output. This is due to the following equation
[2]:
1
cos 2 x = (1 + cos(2x))
2

Index Terms— frequency multiplier; frequency tripler; K-band
1
cos 3 x = (cos(x) + cos(x) ∙ cos(2x)) =
I. INTRODUCTION
There are several frequency multiplying techniques for
generating harmonic frequencies from a fundamental input
frequency. For example frequency doublers can be designed by
exploiting the square-law current–voltage characteristic of fieldeffect transistors (FETs) or by using antiparallel diodes. The
frequency multipliers such as triplers are more challenging to
design and manufacture. Frequency multipliers, especially highfrequency triplers are offered only by few companies. These
triplers are also custom-made what is associated with high costs.
II. THEORY
The frequency multipliers are used to obtain a certain high
frequency signal. The output signal frequency is an integer
multiple of the input signal frequency. The basic block diagram
of a frequency multiplier is shown in Figure 1.
1
2
2

1
cos(x) + (cos(x) + cos(3x))
4
In order to isolate a number of desired harmonics from the output
signal it is needed to use matched filters.
Frequency multiplier is a circuit that generates a sinusoidal
signal with a frequency n-times (n=2, 3, 4,…) higher than
frequency of the input signal. Multipliers can be divided
according to the action principles [2]:
 Synchronous multipliers base on the principle of the
synchronization by the input signal with frequency f1
from the signal generator. The output resonant
frequencies of the synchronous multiplier oscillations are
close to fn = nf1 , where n = 2, 3, 4,….
 Resonant multipliers operate on the principle of the input
signal distortion by the non-linear components (such as:
transistors, diodes) and the selection of the appropriate
input signal harmonic by the resonant circuit.
Resonant multipliers depended on the non-linear component can
be divided into:
Figure 1. Diagram of a frequency multiplier
In order to obtain the output frequency that is an integer
multiple of the input frequency, a component with non-linear
characteristic should be used. The current dependence for the
multiplier when the voltage is applied can be written by Taylor
series as [2]:
 transistor duplicators,
 duplicators with non-linear resistive two-port networks,
 varactor duplicators.
The basic parameters of frequency multipliers are:
2
3
i = Av + Bv + Cv + ⋯
where:
i - current
v - voltage
978-1-5090-2214-4/16/$31.00 ©2016 IEEE


n-duplication factor:
n=
fout

fin

where:
fin - frequency of the input signal,
fout - frequency of the obtained output signal.

multiplier efficiency is the ratio of the power level of
the output signal P(fn ) to the input signal power level
P(f)
η=
P(fn )
P(f)
(5)
The output power level for the n-th harmonic is specified by
the following equation [4]:
P1
Pn < 2 
n
Figure 3. Casing of nonlinear component
(6)
Along with a multiplication order increases the output power
decreases, so high order multiplication should be avoided.
Additionally the relative frequency difference between the
components ((n − 1)f1 , nf1 , (n + 1)f1 ) decreases at high
multiplication, what is causing the demand for a high resonance
quality factor of circuits and limits the possible tuning range of
multipliers. The output resonant circuit is tuned to a multiple of
the input frequency 𝑛𝑓1 and it is stimulated to oscillate once to
n-periods of the output signal.
III. FREQUENCY TRIPLER DESIGN
The structure of the designed frequency tripler is shown
below. It was assumed that the input frequency is 6 GHz
(C-band), thus output frequency is equal to 18 GHz (K-band).
In order to meet requirements mentioned above, the
appropriate frequency tripler structure was designed. The
diagram of this structure is shown in Figure 2.
TABLE I CASING DIMENSIONS
Inches
Millimeters
Dimension
Min.
Max.
Min.
Max.
A
B
C
D
E
0,0445
0,0169
0,0040
0,0128
0,0128
0,0465
0,0189
0,0080
0,0148
0,0148
1,130
0,430
0,102
0,325
0,325
1,180
0,480
0,203
0,375
0,375
The schematic diagram of the designed frequency tripler is
shown in Figure 4. Two filters at the output of multiplier (after
the non-linear component) are band-pass filters with a center
frequency of 18 GHz. The bandwidth of these filters is 1 GHz.
Both filters are made in microstrip technology and their intended
to transfer the third harmonic of the input signal (18 GHz).
Additionally, the proposed structure includes attenuators
(RCAT 03+) and active components such as amplifiers which
perform the function of matching circuits, and provide the
required power level of the third harmonic at the multiplier
output. The use of the proposed elements enable to increase the
efficiency of the tripling process. In the arrangement of the
designed tripler, monolithic amplifiers are used to amplify the
signal given at their inputs. In the designed circuit the amplifier
AVA-183A+ from Mini-Circuits was applied. These unit
operates in the frequency range from 5 GHz up to 18 GHz.
Figure 2. General structure of the frequency tripler
The frequency tripler circuit includes non-linear element that
is antiparallel diode pair. In fact such element can be considered
as a microwave two-port network, which is connected in series
between the input and output matching circuits and the output
filter. The M/A-COM diodes MA4E2508 were used in this
structure. They can operate up to maximum frequency of
26 GHz. Casing and arrangement of diode model pads are shown
in Figure 3, while in Table 1 the component dimensions are
presented (according to the producer technical documentation).
Both input and output paths of the frequency tripler are matched
to 50 ohms. The output matching and filtering circuits of the
designed multiplier were made mainly in order to obtain
a reduced power level of undesirable harmonics at the multiplier
output.
Figure 4. Schematic diagram of frequency tripler
The proposed tripler structure was manufactured on the
laminate TLX-9-0250-CH/CH Taconic, which is appropriate for
high-frequency applications. The laminate TLX-9 Taconic was
used in the design and execution of microstrip filters due to the
low loss factor δ = 0,0022 and the dielectric constant of the
substrate Ԑ𝑟 = 2,5. The relative dielectric Ԑ𝑟 of the substrate
influences on the copper path width, where with the increase of
Ԑ𝑟 , the filter size decreases.
Band-pass filters are commonly used in microwave systems
in order to eliminate the adverse interference and
intermodulation products. Due to the limited performance of
capacitors and inductors, the microwave band-pass filters are
most often constructed using strip resonators o volumetric
resonators. The main strip resonators are quarter-wave or halfwave sections of the homogeneous guides, which shall be
shorted or opened at the end. The output band-pass filter was
designed in the asymmetrical stripline technology. The initial
design requirements for the filter were given as follows:

Bandwidth: 17 500 - 18 500 MHz;

The band-stop attenuation: 30 - 40 dB;

Return loss: less than - 20 dB;

Chebyshev characteristics with waviness of 0.2 dB;

Input and output impedance matched to 50 Ω filter.
Figure 7. Model of the frequency tripler
Test results for the input signal of 6 GHz frequency and
5 dBm input power are shown in Figure 8. The output power
level after the filter for the third harmonic is equal
to -19,58 dBm. The undesirable reproduced harmonics are
filtered and their power level is reduced to -74 dBm.
The simulation results for the band-pass filter are shown in
Figure 5.
Date: 3.JUN.2015
09:27:38
Figure 8. Spectral-response characteristic at the output of frequency tripler for
fin= 6 GHz and Pin= 5 dBm
Figure 5. Simulation results for the band-pass filter
Figure 6 shows the microstrip filter structure manufactured on
a digital milling machine "Quick Circuit".
Figure 9 shows the characteristics of the output power level
in function of the input power level for three harmonics
produced by the frequency tripler circuit. This diagram
illustrates the operation of the multiplier. Filters suppress the
undesired harmonics properly to a level below -75 dBm. The
third harmonic is transmitted with no significant attenuation.
The output power level increases with the increase of the input
power level and reaches a maximum (-16,10 dBm) for the input
power Pin = 10 dBm.
Figure 6. Band-pass filter 18 GHz in microstrip technology
The frequency tripler structure is divided into separate
functional units. This action allows to evaluate the impact of
each individual unit on the key performance of the designed
tripler. The frequency tripler circuit was tested. For this purpose
all individual functional units were connected through the SMA
connectors. The final model layout is shown in Figure 7.
Figure 9. Output power characteristics as a function of the input power of the
frequency tripler for the three harmonics (I harmonic, II harmonic, III
harmonic)
The circuit was made on a common substrate. For this purpose,
the printed circuit board was designed in the Altium Designer.
Figure 10 presents the view of the PCB with the placement of
components on the board in the configuration of Altium's 3D.
Figure 10. Location of components on a PCB (3D view)
Designations in Figure 10 are in accordance with the schematic
diagram shown in Figure 4.
IV. CONCLUSION
The main purpose of this article was to present the structure
and the basic principles of the frequency multiplier. The
laboratory model of such frequency tripler generating 18 GHz
output signal was designed and manufactured. The presented
circuit can be used as a signal microwave source in the
transceiver devices dedicated for radar applications operating in
the upper frequency ranges of Ku-band or lower ranges of
K-band. The final model of the presented tripler was made on
the common substrate, which allowed to eliminate SMA
connectors and gave the ability to integrate the structure in
a single housing.
REFERENCES
[1]
S. Maas, Nonlinear Microwave circuits, Artech House, 1998.
[2]
J. Boksa, Analogowe układy elektroniczne, wyd. BTC Warszawa 2007.
[3]
A. W. J. Chramiec, Mikrofalowe mieszacze diodowe, WKŁ,
Warszawa 1975.
M. T. Faber, J. Chramiec, M. E. Adamski, Microwave and MillimeterWave Diode Frequency Multipliers, Artech House, Norwood 1995.
[4]