Chapter 2 Compensated Marchand balun
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 applied, the results can be seen in Figure 3.1-2 (b). For harmonics (n) of LO signal and harmonics (m) of RF signal, the relationship of current between each diode in Figure 3.2-1 can be expressed as follow:
( )
Therefore, the IF output currents iif1 and iif2 can be expressed as follow
When (m,n)=(1,-1),iif1=iif2=2id1. The total IF output current iif is 4id1 which can be obtained in the sum port of the transformer. When m is even or n is even,iif1 and iif2 are zero. Therefore, the double-balanced mixer has no spurious responses that involve the even harmonics.
3.3 Realization of the Broadband LTCC double-balanced mixer
To implement the broadband LTCC double-balanced mixer, the broadband transformers discussed in Chapter 2 are the key components. The Marchand balun, which has several versions, is the most commonly used component in broadband double-balanced mixer. Tight coupling can be obtained by placing the coupled line in a broadside manner and by using spiral-type coupled lines, the size of quarter-wave line based integrated passive components is decreased. As a result, the required surface area could be reduced. In addition, the spiral-type coupled lines contribute to the minimization of the thickness of the substrate. Therefore, spiral broadside coupled stripline structure achieves required characteristic impedance with thinner dielectric thickness than broadside coupled stripline structure as shown in Figure 3.3-2.
Because of the increasing magnetic flux, the spiral-type transmission line has a larger inductor value than the straight-type transmission line for the same line length.
Therefore, the spiral broadside coupled stripline has larger even mode impedance than straight broadside coupled stripline. Figure 3.3-1 shows the lumped element equivalent circuit of symmetrical coupler. Equation (3.10) and (3.11) are the formulas
of the even and odd mode impedance for symmetrical coupler.
Figure 3.3-1 Lump element equivalent circuit of the symmetrical coupler
m
Dimension BCS SBCS
S [µ ] m 74 74
B [µ ] m 1588 888
Table 3.1 Dimension comparison between BCS and SBCS
Table 3.1 shows the dimension comparison between BCS and SBCS. It indicates that the same coupling (-3.5dB) can be achieved by using spiral broadside coupled stripline with minimum thickness of the substrate. Figure 3.3-2 shows the implemented Marchand balun that consists two identical broadside coupled stripline having 2 turns and fabricated with LTCC technology using conductor linewidth of 100μm and gap of 180μm. The ceramic substrate of the LTCC has the dielectric constant of 7.8 and the coupled-line ground plane spacing of 888µ as shown in m Figure 3.3-3(b). In this spiral broadside coupled stripline, the gap and the linewidth ratio is about 2:1. From the EM simulated results in the spiral broadside coupled stripline, the even mode phase velocity is faster than odd mode phase velocity. As discussed in Chapter 2, we can add a short compensated transmission line (900µm×100µm) to slow down the even mode phase velocity as shown in Figure 3.3-2 (a). Furthermore, the compensated technique can decrease the coupling between adjacent coupled line segments. The coupling between adjacent coupled line segments will degrade the bandwidth of the Marchand balun.
(a) Spiral broadside
coupled stripline Compensated transmission line
B
407µm S=74µm 407µm
(b)
Figure 3.3-2 LTCC Marchand balun (a) Top view of the LTCC Marchand balun (b) Side view of the Marchand balun
Ground planes
Figure 3.3-3 3D structure of the LTCC Marchand balun
Figure 3.3-3 shows the 3D structure of the LTCC Marchand balun that is implemented by two spiral broadside coupled stripline. Two spiral broadside coupled
stripline in the same plane not only increases the even mode and odd mode ratio, but also reduces the layers of the LTCC mixer. Therefore, the lower cost can be obtained.
For straight broadside-coupled stripline with linewidth of 100µ and gap between m two couplers of 74µ , the even mode and odd mode impedance are 96 and 24 , m respectively. For spiral broadside coupled stripline shown in Figure 3.3-2, the even mode and odd mode impedance are about 135
Ω Ω
Ωand 27Ω, respectively.
4
λ/ λ/4
2
5 6
dB
Figure 3.3-4 Simulated results of the Marchand balun
The simulated results of the LTCC Marchand balun was obtained using EM simulator (Sonnet). The unbalanced input impedance is 50Ω and the balanced output impedance is 70Ω. Figure 3.3-4 shows that the S11 is less than –10dB in the range of 2.3 to 6.15GHz. The differences of the amplitude and phase between the balanced
output ports are shown in Figure 3.3-5. The amplitude imbalance at balanced output ports is within 1dB, and the phase imbalance at balanced output ports is less than over the frequency range of 2.3 to 6.15GHz where |S
10o
11|< -10dB.
Amplitude unbalance (dB) Phase unbalance (degree)
Figure 3.3-5 Simulated results of the amplitude unbalance and the phase unbalance Figure 3.3-7 shows the S11 is less than –10dB in the range of 2.5 to 6.6GHz. The differences of the amplitude and phase between the balanced output ports are shown in Figure 3.3-8. The amplitude imbalance at balanced output ports is within 1dB, and the phase imbalance at balanced output ports is less than over the frequency range of 2.5 to 6.15GHz where |S
10o
11|< -10dB. The capacitors serve as the lowpass filter for IF signals and the high pass filter for RF signals. The IF signals can be obtained as shown in Figure 3.3-6. The performance of the Marchand balun was degraded by the capacitors.
4
λ/ λ/4
4 3 1
IF output
7 8
Figure 3.3-6 Schematic of the Marchand balun with IF output
dB
Figure 3.3-7 Simulated results of the Marchand balun
Amplitude unbalance (dB) Phase unbalance (degree)
Figure 3.3-8 Simulated results of the amplitude unbalance and the phase unbalance
Designing the optimum capacitors is extremely important for the IF signal. When the capacitor value is too large, it will degrade the conversion loss of the higher IF frequencies. When the capacitor value is too small, two short-circuited section aren’t
perfect grounding at the RF frequencies. Therefore, the amplitude unbalance and the phase unbalance of the Marchand balun are poor.
3 5 Diodes
2
6
Capacitor
Ground planes Ground
planes IF
2
1
Two Marchand baluns
Figure 3.3-9 3D structure of the double-balanced mixer
The 3-D structure of the double-balanced mixer is shown in Figure3.3-9. The diodes will be mounted on the top of the LTCC component. The Schottky diode-quad such as Metelics MSS-40, 455-B40 can be used as mixing elements. The chip size of the LTCC double- balanced mixer is4800µm×3400µm×962µm.
3.4 Simulated results of the double-balanced mixer
The simulated results of the double-balanced mixer were obtained using the circuit simulator (Agilent ADS). Because the circuit is symmetrical, we can exchange the RF and LO ports. Figure 3.4-1 shows that conversion loss is less than 8dB in the RF frequency range of 2.4 to 6.4GHz. Figure 3.4-2 shows that conversion loss is less than 8dB in the RF frequency range of 1.75 to 6.5 GHz.
0 Figure 3.4-1 Conversion loss vs. RF frequency for RF balun center tap
IF=300MHz,PLO=14dBm IF=300MHz,PLO=14dBm
Figure 3.4-2 Conversion loss vs. RF frequency for LO balun center tap
Figure 3.4-3 and Figure 3.4-4 show the RF-IF, RF-LO and LO-IF isolation of the LTCC mixer. The LO-RF isolation and LO-IF isolation for the center tap of the RF secondary served as the IF output are good as discussed in Chapter 3.2. For the center tap of the RF secondary served as the IF output, the RF-IF isolations over the frequency range of 1.5 to 2.8GHz are poor. The same result (LO-IF isolation) can be obtained for the center tap of the LO secondary served as the IF output. The main factor is the design of the capacitor. For the center tap of the RF secondary served as the IF output, the capacitors aren’t perfect grounding for RF signals at low frequencies. Hence, the RF-IF isolation isn’t good at lower frequencies. Increasing capacitor values will improve the RF-IF isolation, but degrade the conversion loss of the IF signal.
0 10 20 30 40 50 60 70 80
1 2 3 4 5 6 7
RF frquency(GHz)
isolation(dB)
8 RF-IF RF-LO LO-IF
Figure 3.4-3 LO-IF, LO-RF, RF-IF isolation vs. RF frequency for RF balun center tap
0
Figure 3.4-4 LO-IF, LO-RF, RF-IF isolation vs. RF frequency for LO balun center tap
0
Figure 3.4-5 Conversion loss vs. IF frequencies for RF balun center tap
Figure 3.4-5 shows the IF bandwidth of the LTCC double-balanced mixer. The capacitors restrict the IF bandwidth. The larger IF results in larger conversion loss.
Chapter 4
Combline Filter with Capacitive Cross-coupling
4.1 Theory of the typical combline filter
A typical tapped combline filter is shown in Figure 4.1-1[16-20]. The lines are each short circuited to ground at the same end while opposite ends are terminated in lumped capacitors. As the capacitors are increased the shunt lines behaves as inductive elements and resonate with the capacitors at a frequency below the quarter- wave frequency. At the resonant frequency of the filter, the lines are significantly less than a quarter wavelength length. Thus, the larger the loading capacitances, the shorter the resonator lines, which results in a more compact filter structure with a wider stopband between the first passband and the second passband. If the capacitors are not present, the resonator line will be λ0/4 long at resonance, and the structure will have no passband. This is because the magnetic and electric couplings totally cancel each other out in this case.
In this type of filter, the second pass band occurs when the resonator line elements are somewhat over a half-wavelength long. So, if the resonator lines are
8
0/
λ long at the primary passband, the second passband will be centered at somewhat over four times the midband frequency of the first passband. If the resonator line elements are made to be less thanλ0/8 long at the primary passband, the second passband will be even further removed.
‧‧‧‧‧
Figure 4.1-1 Typical combline bandpass filter
1 2
Figure 4.1-2 Transformation of equivalent circuit of coupled line
θ
Figure 4.1-3 Schematic of J-inverter
input
Figure 4.1-4 Equivalent circuit of the combline filter
‧‧‧ CN
Figure 4.1-5 J inverter equivalent circuit for the combline filter
Figure 4.1-6 Lump element equivalent circuits of the combline filter
…
Figure 4.1-2 can be equivalent to a J-inverter with J = Y0cotθ while
as shown in Figure 4.1-3. Then, the combline filter in Figure 4.1-1 can be convert to the equivalent circuit as shown in Figure 4.1-4. The J inverter equivalent circuit for the combline filter is shown in Figure 4.1-5. Figure 4.1-6 is the lump element equivalent circuits of the combline filter.
90o
θ ≠
4.2 Phase relationships
Let the phase component of the Y-parameter S21 be denoted Φ21. Consider the series capacitor of Figure 4.2-1(a) as two port devices. The signal entering port 1 will undergo a phase shift upon exiting port 2. This is Φ21, and it tends toward . For the series inductor as shown in Figure 4.2-1(b), the phase shift is . For the shunt inductor/capacitor pairs in Figure 4.2-1(c), the phase shift at off-resonance frequencies is dependent on whether the signal is above of below resonances. For signals below the resonance frequency, the phase shift tends toward . However, for signals above resonance frequency, the phase shift tends toward .
90o
+ 90o
−
90o
+ 90o
−
The three-resonator structure of Figure 4.3-1 and Figure 4.3-2, which represents a cascaded triplet (CT) section using a capacitive cross-coupling between resonators 1 and 3. Path 1-2-3 is the primary path, and path 1-3 is the secondary path that follows the capacitive cross-coupling. In Figure 4.2-2(a), the phase shifts for two paths are given in Table 4.1. Above resonance, the two paths are in phase, but below resonance, the two paths are out phase. This destructive interference causes a transmission zero on the low-side skirt as shown in Figure 4.2-2(b). Stronger coupling between 1 and 3 causes the zero to move up the skirt toward passband. Decreasing the coupling moves it farther down the skirt.
Port 2 Port 1
Y=jωC
Φ21=+90∘
(a)
Port 2
Port 1 Φ21=-90∘
Y=-j(1/ωL)
(b)
Φ21=ang(Y21)
Resonant frequency -90∘
90∘ Port 2
Port 1
(c)
Figure 4.2-1 Phase shifts for series capacitor, series inductor and shunt inductor/capacitor pairs (a) Series capacitor, (b) Series inductor, (c) Shunt inductor/capacitor pairs
90∘
90∘ 90∘
+/- 90ο
3 2
1
dB
(a) (b)
Figure 4.2-2 CT section (a) Multi-path coupling diagram for CT section with capacitive cross-coupling (b) Possible frequency response
Below Resonance Above Resonance
90+90+90 = 270° 90-90+90=90°
90° 90°
Path 1-2-3
Result Path 1-3
In phase Out phase
Table 4.1 Total phase shifts for two paths in a CT section with capacitive cross-coupling
4.3 Design of the LTCC three-poles combline filter with cross-coupled capacitor
To meet the specifications in Table 1.1, the filter should generate the zero at 2.1GHz. As discussed in Chapter 4.2, we can design a CT-type filter using a capacitive cross-coupling between resonators 1 and 3 to generate the zero in the low-side skirt. The proposed structure in this design is shown in Figure 4.2-1, which shows the combline filter with cross-coupled capacitor modified from the typical combline filter. The coupling between adjacent resonators can be tuning easily with the direct-coupled capacitors. Edge coupling has restricted the bandwidth of the typical combline filter. The modified combline filter can achieve larger bandwidth
than typical edge-coupled combline filter through the direct-coupled capacitors.
Figure 4.3-2 shows the equivalent circuit of the modified combline filter.
SL3
Figure 4.3-1 Modified combline filter
C10 C20 C30
Figure 4.3-2 Equivalent circuit of the modified combline filter
Step 1: Choose the optimum loading capacitors for this design. The larger the loading capacitances, the shorter the resonator lines, which results in a more compact filter structure with a wider stopband between the first passband and the second passband. However, the circuit dimension restricts the values of the
MIM capacitors.
Step 2: Design the inductors of the resonators using transmission lines and these resonators resonate at 2.45GHz.
Step 3: Choose C12, C23, and C13 to meet the specifications in Table 1.1.
Step 4: Fine-tune all component values.
The corresponding component values in Figure 4.3-1 are C10 = C30 = 4.18 pF, C20 =3.93 pF, C12 = C23 = 0.9 pF, C13=0.319 pF and the length and width are 73 mil×6 mil for SL1, SL2 and SL3. Figure 4.3-3 shows that the simulation results using the circuit simulator (AWR Microwave Office). Figure 4.3-3 indicates that the low-side skirt zero is at 2.1GHz and return loss in the passband (2.4-2.5GHz) is less than –30dB.The filter also suppress the second harmonic, third harmonic and all the lower stopband signals. This design meets the specifications of the Table 1.1.
dB
Figure 4.3-3 Simulated response of the combline filter with Microwave Office
Dgree
Figure 4.3-4 Applying Y-parameter to analyze the transmission zeros
SL1 SL2 SL3
I/O port I/O port
C13
C23 C12
C30 C10 C20
Figure 4.3-5 Combline filter and cross-coupled capacitor
These transmission zeros occur at the frequencies where of and of the reminder part of the filter has the same magnitude, but opposite phase as shown in Figure 4.3-4 and Figure 4.3-5. This means that of the three-pole combline filter with capacitive cross-coupling at these frequencies will be zero. The location of zero
These transmission zeros occur at the frequencies where of and of the reminder part of the filter has the same magnitude, but opposite phase as shown in Figure 4.3-4 and Figure 4.3-5. This means that of the three-pole combline filter with capacitive cross-coupling at these frequencies will be zero. The location of zero