In recent years, the wireless communication market has experienced explosive growth. There is increasing demand to make portable communication systems lighter, more compact, and better functionality. The ceramic multilayer substrate technology such as LTCC (Low temperature cofired ceramics) enables the creation of monolithic, three-dimensional, cost-effective microwave circuits and modules [1-5]. Monolithic LTCC structures incorporating buried components and surface-mounted components allow increased design flexibility by providing a mechanism for establishing microstrip, stripline, coplanar waveguide and DC lines within the same medium.
Additionally, the reduced weight of LTCC packages and the low loss characteristics of the dielectric and conductors make LTCC an ideal candidate for high performance commercial and military electronic systems. Integrated passive components such as filters, couplers, baluns and impedance transformers are usually based on transmission line sections of quarter wavelengths. Hence, the sizes of these circuits are large at low frequencies.
Today’s wireless telecommunication for dual-band applications such as IEEE802.11a (5.2GHz, 5.7GHz) and 802.11b (2.4GHz) wireless LAN have increased rapidly. The broadband characteristic of the balun has the potential to provide various wide-band applications such as broadband mixer [6-14]. Recently, monolithic Marchand baluns have been revisited and shown to be feasible in wireless communication applications. However, they suffer from high amplitude and phase unbalance at output ports.
Figure 1-1 shows the balanced diplexer module that will be implemented and integrated by LTCC technology for wireless local area network (LAN) applications.
The diplexer module will meet the specifications of IEEE 802.11a(5.2GHz、5.7GHz) and 802.11b(2.4GHz) wireless LAN. In the wireless LAN applications, the image signal needs to be highly attenuated to maintain the high quality signal received from the antenna. Moreover, the leakages of harmonics from the transmitted circuit appearing in the received circuit must be suppressed. Using the technique of cross-coupling to produce transmission zeros, the rejection below the passband is increased. This can reduce the number of resonating elements required to meet a specification and this, in turn, reduces the insertion loss, size, manufacturing cost of the design and tuning time. Therefore, the filter with the characteristic of having transmission zeros at the low-side skirt can generate a high attenuation rate and suppress all the lower stopband signals. The filter with broad stopband and transmission zeros at the high-side skirt can suppress the second harmonic and third harmonic.
The SIR (Stepped Impedance Resonators) filter [15] and combline filter [3, 16-20] have the characteristic of broad stopband due to the destruction of the periods of resonators. However, the combline filter has more compact size than the SIR filter.
Therefore, it has been widely used in wireless communication systems.
SW
Figure 1-1 LTCC balanced diplexer module for wireless LAN applications
Specification 5GHz band 2.4GHz band Frequency band 4.9~5.9GHz 2.4~2.5GHz
Input impedance 50 ohm 50 ohm
Output impedance 50 ohm 50 ohm
BPFs rejection 30dBc @ 0.5GHz~4GHz 20dBc @ 4GHz~4.5GHz 30dBc @ 9.8GHz~11.8GHz 20dBc @ 14.7GHz~17.7GHz
30dBc @0.88GHz~1.785GHz 35dBc @ 1.85GHz~1.91GHz 30dBc @ 2.1G
30dBc @ 4.8GHz~5GHz 20dBc @ 7.2GHz~7.5GHz
Table 1.1 Specifications of the filters for wireless LAN
In Chapter 2, the Marchand balun has been implemented by two substrates.
However, it suffers from high amplitude and phase unbalance at output ports. Adding a short transmission line between two microstrip broadside coupler to compensate the difference between even mode and odd mode phase velocity is proposed.
In Chapter 3, we will develop the broadband double-balanced mixer with LTCC technology. The ceramic substrate of the LTCC has dielectric constant of 7.8. To achieve broad bandwidth in designing the double-balanced mixer, broadband baluns are the key components in the mixer. In this design, using spiral broadside coupled stripline to implement the Marchand balun has more compact size. However, the same phenomenon can be found in the spiral broadside coupled stripline discussed in Chapter 2. Therefore, we also compensated the even and odd mode phase velocities with a transmission line.
In Chapter 4, the three-pole combline filter with cross-coupling is proposed.
Table 1.1 shows the specifications of the filter in Figure 1-1. The LTCC dielectric constant is 33 and each layer thickness is 1.2mil. Therefore, we can minimize the circuit as small as possible.
In Chapter 5, the substrate and the shielding box effects for the three-pole combline filter with cross-coupling are discussed.
Chapter 6 is the conclusion.
Chapter 2
Compensated Marchand balun
Baluns are key components in balanced circuit topologies such as double- balanced mixers, push-pull amplifiers, frequency doublers, antenna feed networks and phase shifters. The word balun is an acronym for balanced-to-unbalanced converter, and the function is employed to change an unbalanced signal to a balanced signal with equal potential but opposite polarity. The four-port passive circuits, such as rat-race hybrids and waveguide magic tees, can be used as baluns. Major limitations of these components are their narrow bandwidths and the lack of a method for center-tap grounding. Most coupled lines based baluns require a high even mode to odd mode impedances ratio, one order of magnitude or more. This results in good balance and reasonable bandwidth. The Marchand balun has a better bandwidth and more balanced outputs than the coupled line baluns because the smaller difference between the even and odd mode impedance compared with what is needed for the coupled line balun case. Proper selection of balun parameters can achieve a bandwidth of more than 10:1.
The Marchand balun is perhaps one of the most attractive due to its planar structure and wide-band performance [6-7]. Beside, multilayer configurations make MIC/MMIC more compact and can exhibit wide bandwidths due to tight coupling in coupled line baluns [8-14].
2.1 Analysis of the Marchand balun
The Marchand balun is a derivative of one of the first balun configurations that was physically realized in a coaxial configuration as shown in Figure 2.1-1(a). The equivalent transmission line model for the Marchand balun is shown in Figure 2.1-1(b).
= 900 at fo
Z
0Z
S1θ θ
Z
S2Z
BZ
1Z
R
L(a)
ZB
ZS2
ZS1
Z1
Z2
Z0
ZL
(b)
Figure 2.1-1 Marchand balun (a) Coaxial cross section
(b) Equivalent transmission line model
The Marchand balun basically consists of an unbalanced, an open-circuited, two short circuited, and balanced transmission line sections as shown in figure 2.1-2. Each section is about a quarter-wavelength long at the center frequency of operation. The Marchand balun consists of two coupled sections, which may be realized using microstrip-coupled lines, Lange couplers, multilayer coupled structures, or spiral coils.
Phase shifter A [S21 phase]
Phase shifter B [S31 phase]
Phase shifter A + Phase shifter B
|S31 phase-S21 phase|=180o
Balanced output
Figure 2.1-2 Basic logic of the Marchand balun
Port2
Figure 2.1-3 Schematic of the symmetrical Marchand balun as two identical
Figure 2.1-3 shows the schematic of the Marchand balun as two identical couplers. For symmetrical baluns, the scattering matrix of the balun can be derived from the scattering matrix of two identical couplers. The unbalanced input impedance is Zo and the balanced output impedance is Z1. If the source impedance and load impedances are equal to Zo, the scattering matrix for ideal couplers with infinite directivity and coupling factor C is given by
(2.1)
Then, the S-parameters of the balun in Figure 2.1-3 are then given by (2.2) from [6].
[ ]
Equation (2.2) shows that the use of identical coupled sections results in balun outputs of equal amplitude and opposite phase, regardless of the coupling factor and port terminations. To achieve optimum power transfer of –3dB to balanced port, we require
With (2.2) and (2.3), the required coupling factor for optimum balun performance is give by
With equation (2.4), we can design the Marchand balun by determining one of two variables and the other can be obtained. If we choose all the ports are terminated with 50Ω, the required coupling factor is –4.8dB. Then, the coupled line will be designed to meet the required coupling factor.
2.2 Realization of the Marchand balun
To increase the even mode and odd mode impedance ratio, we implemented the Marchand balun with microstrip broadside couplers. The Marchand balun was
fabricated using Rogers 4003(εr=3.38) with multilayer structures. The substrate consists of 2 layers, the lower layer of 20mil and the upper layer of 8mil as shown in Figure 2.2-1(b). Figure 2.2-1 shows the side view and the top view of the implemented Marchand balun. The dimensions for the various line sections are input line A has a 16 mil line-width and is 447 mil long. The line width, length for the open-circuited line B and short-circuited lines C are 24 mil, 447 mil and 30 mil, 447 mil, respectively. The unbalanced input impedance is 50Ω and the balanced output impedance is 50Ω.
Figure 2.2-1 Realization of the Marchand balun (a) top view of the Marchand balun (b) side view
Figure 2.2-2(a) shows the equivalent transmission line model of the Marchand balun in Figure 2.2-1(a). Corresponding values of the transmission line model are:
Ω
Figure 2.2-2(a) Equivalent circuit in this design (b) Return loss of the transmission line model in (a)
dB
Figure 2.2-3 Simulated results of the Marchand balun
Amplitude unbalance (dB) Phase unbalance (degree)
Figure 2.2-4 Simulated results of the amplitude unbalance and the phase unbalance
The balun has been simulated on a full-wave EM simulator (Sonnet). Figure 2.2-3 and Figure 2.2-4 show the amplitude unbalance at balanced output ports is within 1dB,and the phase unbalance at balanced output ports is less than over the frequency range of 1.6 to 4.8GHz where |S
10o
11|< -10dB.
2.3 Realization of the compensated Marchand balun with a short transmission- line From the simulated results in Figure 2.2-3 and Figure 2.2-4, the phase and amplitude balance of the Marchand balun are poor. The main reason for the poor balance is the difference between even mode and odd mode phase velocity (Stringently speaking, the normal mode of the broadside microstrip coupler are c mode and π mode). However, the results of the even and odd mode excited method meet the coupling of the couplers. Beside, several papers [2,8] also simplify c mode and π mode as even mode and odd mode. Therefore, we explain the mechanism of the Marchand balun with even and odd mode. The coupled electrical length θ, even mode transmission phase θe and odd mode transmission phase θo are given by
where ω is the operation frequency, L is the physical length of coupled line, and are the even mode and odd mode phase velocities, respectively. For the microstrip broadside structure, because the even mode phase velocity is always faster than odd mode phase velocity,
e
Vp Vpo
θo is always larger than θe for all frequencies as shown in Figure 2.3-1. Therefore, the difference between the even mode and odd mode phase velocity degrades the bandwidth of the Marchand balun.
Compensation for the difference in normal mode phase velocity in the broadside-coupled structure is required. Adding capacitors at four ends of the couplers in [2] is effective in improving the difference between the even mode and odd mode phase velocity. But it needs too many capacitors for compensation. Therefore, compensation is accomplished by connecting a short transmission line to a pair of couplers. The short transmission line acts like placing the capacitor to ground (see
Figure 2.3-2), instead of between the plates, would have the effect of “slowing down”
the even mode phase velocity. As shown in Figure 2.3-1, the dot lines are the transmission phases of the even mode and odd mode in the uncompensated coupler and the solid lines are the transmission phases of the even mode and odd mode in the compensated coupler. Adding the capacitor in one end is effectively in improving the difference between the even mode and odd mode phase velocity.
Transmission phase (Degree)
Figure 2.3-1 Even mode and odd mode transmission phase vs. frequency
1 2
4 3
Figure 2.3-2 Circuit diagram of proposed topology
The Marchand balun can be modified as shown in Figure 2.3-3. We add the short
transmission line between two couplers. The dimensions of the modified Marchand balun and the Marchand balun in Figure 2.2-1 are the same except the middle transmission line. Figure 2.3-4 shows the proposed 3-D structure of the Marchand balun.
Via
Via
65mil 65mil
Balanced output Unbalanced input
Compensated transmission line
Top
Bottom metal
Figure 2.3-3 Top view of the compensated Marchand balun with a short transmission line
Figure 2.3-4 3-D structure of the proposed Marchand balun
0.8 0.9 1 1.1 1.2
40 45 50 55 60 65 70 75 80
transmission line impedanc
Normalized bandwidth
e
65mil zo
2 3 1
∆f /fo
zo (Ω)
Figure 2.3-5 Operational bandwidth of the compensated Marchand balun.
Figure2.3-5 indicates the operational frequency of the compensated Marchand balun as a function of transmission line impedance. The bandwidth is defined as the frequency range yielding the amplitude difference within 1dB, the phase unbalance within10o and |S11|< -10dB. These difference result in more than 20-dB suppression of the undesired signal when the balun is in balanced mixers. The bandwidth increases when Zo decrease and is maximum at line impedances from 58 to 46 Ω for the line length of 65mil. Lower line impedances degrade the bandwidth because the amplitude and phase differences caused by the added transmission line are too large to compensate for the differences of the Marchand balun.
Z=71 Z=62
Amplitude unbalance (dB)
Z=55 Z=50
Z=46
Z=42
Figure 2.3-6 Amplitude unbalance with various transmission line impedances
Phase unbalance (degree)
Z=71 Z=62 Z=55 Z=50
Z=46 Z=42
Figure 2.3-7 Phase unbalance with various transmission line impedances
Figure 2.3-6 and Figure 2.3-7 show that the amplitude unbalance and phase unbalance with various transmission line impedances. Although the amplitude unbalance is within 1dB and phase unbalance is less than 5o over the frequency range of 1.6 to 6.21Hz at the line impedances from 58 to 46 Ω, the optimum line impedance
can obtained from Figure 2.3-6 and Figure 2.3-7. The optimum line impedance is about 50Ω for the line length of 65mil. Therefore, we choose the short transmission line (65 mil×65 mil) as our design between two couplers. The simulated responses of the modified Marchand balun are shown in Figure 2.3-8, Figure 2.3-9 and Figure 2.3-10.
dB
Figure 2.3-8 Simulated responses of the Marchand balun
Degree
Figure 2.3-9 Simulated phase responses of the Marchand balun
Amplitude unbalance (dB) Phase unbalance (degree)
Figure 2.3-10 Simulated results of the amplitude unbalance and the phase unbalance
Amplitude unbalance (dB) Phase unbalance (degree)
Figure 2.3-11 Simulated results of the amplitude unbalance and the phase unbalance for compensated and uncompensated Marchand balun
From the simulated results shown in Figure 2.3-8, the S11 is less than –10dB in the range of 1.6 to 6.1GHz. The differences of the amplitude and phase between the balanced output ports are shown in Figure 2.3-10. The amplitude unbalance at
balanced output ports is within 0.5 dB, and the phase unbalance at balanced output ports is less than 3o over the frequency range of 1.6 to 6.1GHz where |S11|< -10dB.
Figure 2.3-11 shows the noticeable improvement in the amplitude balance and phase balance for the Marchand balun with the optimum compensated transmission line.
2.4 Fabrication of the modified Marchand balun
Figure 2.4-1 shows the photograph of the fabricated balun. We add the short transmission line (65 mil×65 mil) between two couplers. To implement the two-layer configuration, we use the plastics screws that have seldom effects to the circuit to fix the two substrates.
Plastics screws
Figure 2.4-1 Photograph of fabricated balun
dB
Figure 2.4-2 Measured responses of the Marchand balun
Degree
Figure 2.4-3 Measured phase responses of the Marchand balun
Phase unbalance (degree)
Amplitude unbalance (dB)
Figure 2.4-4 Measured results of the amplitude unbalance and the phase unbalance
From the measured results shown in Figure 2.4-2, the S11 is less than –10dB in the range of 1.9 to 6.2GHz. The differences of the amplitude and phase between the balanced output ports are shown in Figure 2.4-4. The amplitude unbalance at balanced output ports is within 1dB, and the phase unbalance at balanced output ports is less than 5o over the frequency range of 1.6 to 6.2 GHz where |S11|< -10dB. In Figure 2.3-9 and Figure 2.4-3, the output signals of measured phase responses have more periods than simulated phase responses. This is because the output transmission lines and the SMA connectors are neglected in EM simulation. These neglected components contribute the electrical length for output signals. Hence, the fabricated balun has more periods.
Chapter 3
Broadband LTCC Doubly Balanced Mixer
Figure3.2-1 shows a double-balanced ring mixer. It consists of two transformers and a ring of identical diodes. The advantages over the double-balanced mixer are inherent isolation between all port, rejection of LO noise and spurious signals, rejection of spurious responses and certain intermodulation products, and extremely broadband operation. The disadvantages are the need for four diodes and two hybrids, greater LO power requirements, and generally higher conversion loss than single-diode or singly balanced mixers.
3.1 The property of the Schottky diode
The Schottky diode is a non-linear device. The equivalent circuit and I-V curve can be expressed in Figure 3.1-1. It consists of capacitor C(v), resistor R(v) as a function of the voltage and a fixed series resistor Rs. The non-linear characteristic of R(v) is used in designing mixer. When pumping the Schottky diode with greater local oscillator (LO) power, the signal would be rectified (only the positive cycle can turn on the diode). Hence, the diode current iLO(t) and conductance waveform gLO(t) is shown as Figure 3.1-2. The Fourier series expansion of gLO(t) can be expressed as following.
Because the non-linear characteristic of the diode, the diode involves harmonics of RF frequency when RF signal is applied to the diode at the same time. The Fourier
series expansion of the RF voltage can be given by
The diode current id involves all intermodulation products of the RF frequency and LO frequency. The terms which (m,n) equals (1,-1) or (-1,1) are the desired signals(IF signals). The low pass filter can eliminate all other higher order terms.
Rs
(a) The equivalent circuit of the diode (b) I-V curve of the diode Figure 3.1-1 Equivalent circuit and I-V curve of a diode
t
(b) Conductance waveform (a) Current waveform
Figure 3.1-2 Current and conductance waveform of the diode
3.2 Analysis of double-balanced ring mixer
Figure 3.2-1 Analysis of double-balanced ring mixer
Vd1
Figure 3.2-2 Voltage and current waveform of the diodes (a) LO voltage and current (index:n) (b) RF voltage and current (index:m)
The RF signal is applied to the primary of one transformer, and the LO is applied to the primary of the other. The center tap of the LO transformer’s secondary is grounded, and the center tap of the RF secondary serves as the IF output. (In theory, the LO center tap could be used for the IF output, but the LO-to-IF isolation, which is usually more critical than the RF-to-IF isolation. This is because LO signal power is larger than RF signal power. In general, the LO signal power for double balanced mixer is above 10dBm.) If two identical loads are connected in series across the entire transformer’s secondary as shown in Figure 3.1-1, their connection point is also a virtual ground. In Figure 3.1-1 the points A and A’ are virtual grounds for the LO signals, and B and B’ are virtual grounds for the RF signals. Since the RF transformer’s secondary is connected to the LO virtual-ground nodes and the LO transformer’s secondary is connected to the RF virtual grounds. Therefore, the LO-to-RF isolation is theoretically infinite. Also, one can ignore the RF transformer while examining the LO circuit, and vice versa.
When LO power is applied, an AC LO voltage is applied to the nodes B and B’.
When B is positive and B’ is negative, the diodes D1 and D2 are turned on. D3 and D4 are reverse biased. They are reverse biased by a voltage equal to the forward turn-on voltage of the other pair, and enough to make them effectively open circuits.
In the next half-cycle of LO voltage, D3 and D4 are turned on and D1and D2 are off.
Figure 3.1-2(a) indicates the results when LO power is applied. When RF power is
Figure 3.1-2(a) indicates the results when LO power is applied. When RF power is