Chapter 2: A wideband 3-dB directional coupler
2.6 Three-section coupler – measurement
The photograph of the proposed three-section directional coupler is shown in Figure 2.6-1. The circuit is fabricated on a Al O substrate with a dielectric constant of 9.8 and thickness of 15 mil. The measurement result is shown in figure 2.6-2
Figure 2.6-1 Photograph of the fabricated three-section 3-dB directional coupler
Figure 2.6-2 Measured response of the proposed hybrid
As can be seen in figure 2.6-2, the coupling is slightly greater than through and the reason has been discussed previously. The measured amplitude balance between port 2 (through port) and port 3 (coupled port) is shown in figure 2.6-3. The measured amplitude error is better than 0.75dB over the designed frequency of 2-6 GHz.
Figure 2.6-3 Measured amplitude errors of the proposed directional coupler
Figure 2.6-4 Measured phase inbalance of the proposed directional coupler
The measrued phase error is shown as above. The phase balance is about 88 2 . The phase of the coupled and direct port has a 90 degree difference due to its symmetric.
Because the non-uniform coupler in the center section is used (mender ground), the circuit will not be perfect symmetric. Hence the phase error is a little bit larger.
The meander ground in center section provide good impedance matching between different sections at all desired frequency band. Good impedance matching is the main difference between traditional coupler and the proposed coupler. It is usually the reason why we can get better performance only when they simulate the coupler individually and cascade them to get the result, but the performance get worse at high frequency when they simulate it as a whole.
Chapter 3
Wilkinson power divider
In order to make IQ mixer operate appropriately. A three port device with two output signal has equal phase and amplitude is required. The T-junction and wilkilson power divider [9] is commonly used. T-junction’s two ouput ports has no isolation and if the resistive divider is used, there are some extra loss have to be consider. Hence the wilkinson power divider become the best choose for the IQ mixer.
Because the circuit is fabricated with coplanar waveguide (CPW) structure, it has more advantages than microstrip based wilkinson power divider. The coupling between two quarter wavelength transmission line can be reduce by the ground of CPW. Hence a small circuit size can be achieve and the difficulty of circuit design is diminished.
3.1 Theory
The wilkinson power divider is a three-port device with a scattering matrix of:
S
Note this device is matched at port 1 (S 0), and we find that magnitude of column 1 is:
|S |+|S |+|S |=1
Thus, just like the lossless divider the incident power on port 1 is evenly and efficiently divided between the outputs of port 2 and port 3:
P |S | P P
2 P |S | P P 2
We also note that the port 2 and 3 of this device are matched. S S 0
The resister is the secret to the Wilkinson power divider, and is the reason that it is matched at ports 2 and 3, and the reason that port 2 and port 3 are isolated. Single section Wilkinson power divider can reach 60% fractional bandwidth. In order to increase the bandwidth of the power divider, we used muti-section struction again.
3.2 Design procedure and realization
S. B. Cohn has provided some tables for designing multi-section wilkinsion power divider [10]. A 100% bandwidth with return loss and isolation around -27dB can be achieve by a three-section structure. Unfortunately, we can’t afford more room for such long structure. By preliminary studies, we decided to used two section Chebyshev response structure. On one hand, it won’t be too long; on the other hand, the performance is acceptabe. The circuit-level simulation is carried out by Advanced Design System 2009 and we get EM simulation result from Sonnet. This power divider is fabricated on a Al O substrate with a dielectric constant of 9.8 and thickness of 15 mil. The dimension of each section is shown in figure 3.1-1.
Figure 3.2-1 The design parameters of two-section wilkinson power divider
The EM simulation result is shown in figure 3.2-2. The return loss (S ) and isolation (S ) is below -21dB for the desired frequency band which is still acceptable.
Because the wilkinson power divider is a symmetry structure, the amplitude balance and phase balance is guaranteed to be good which is essential for RF input signal of IQ mixer. The center frequency is a little higher than 4GHz because the length of power divider is shrinked.
Figure 3.2-2 Simulation result of the wilkinson power divider
3.3 Measurement
The measurement result is shown in figure 3.3-1. The return loss and isolation is better than -15dB at the desired frequency band (2-6 GHz) and the through is around -3.1dB. The photograph of the circuit is shown in figure 3.3-2.
Figure 3.3-1 Measurement result of wilkinson power divider
Figure 3.3-2 Photograph of the fabricated two-section wilkinson power divider
Chapter 4
single-balanced mixer
The IQ-mixer contains two balanced mixers and a phase shifting hybrid. General speaking a wideband diode mixer is designed in balanced type structure. The balanced mixer in the construction consists of two identical single ended mixers with a 3dB hybrid junction(90 or 180 degrees) to produce either better input VSWR or better LO/RF isolation. The balanced mixer using a 90o hybrid generates good RF VSWR, but poor LO/RF isolation. Using a 180o hybrid suppress all even harmonics of both LO and RF siganls, thus yielding a very low conversion loss. Among all 180o hybrids. The three-port balun only provides the out-of-phase power splitting without good output port-to-port isolations and return losses. These properties make the rat race ring in the balanced circuits better than the balun.
To achieve compact circuit size and wider bandwidth, the size of the mixer was reduced by using phase inverter in the ring arm. Moreover, the place of the diodes was deposit inside the ring. In this chapter a single-balanced mixer with finite ground CPW (FCPW) on 15 mils Al2O3 substrate is designed and fabricated.
4.1 Theory
A single-balanced diode mixer uses two diodes. Either the LO drive or the RF signal is balanced, adding destructively at the IF port of the mixer and providing inherent rejection. The level of rejection is dependent on the amplitude and phase balance of the balun, providing the balanced drive, and the matching between the two diodes. Other advantages of a singly-balanced design are rejection certain mixer spurious products, depending on the exact configuration, and suppression of Amplitude Modulated (AM) LO noise. AM noise could be a significant problem in early microwave and mm-wave receivers where the available LO sources were very noisy.
Modern wireless transceivers tend to make use of synthesised LO drives and the LO phase noise gives more of a problem than the AM noise.
One disadvantage of balanced designs is that they require a higher LO drive level.
Figure 4.1 shows a block diagram of a single-balanced mixer.
Figure 4.1-1 Block diagram of a single-balanced mixer
The LO drive to the two diodes is in anti-phase and the RF signal is in-phase. If the mixing products are at mRF ± nLO, this mixer will reject all spurious products where m is even. The reason can be seen below. Figure 4.1-2 shows the typical I-V characteristics of a Schottky diode, which can be described by equation (4.1).
I a V a V a V a V (4.1)
Figure 4.1-2 Typical forward I-V Characteristics of a diode
The current through each diode is depicted as below.
I a V a V a V a V
I a V a V a V a V
The minus sign in (4.3) is due to that LO drive to the two diodes is in anti-phase.
V VRcos ωRt VLcos ωLt (4.2) V VRcos ωRt VLcos ωLt (4.3)
The IF current is:
IIF i i a V V a V V a V V a V V … (4.4)
Then replace (4.2) and (4.3) into (4.4).
IIF a 2VRcos ωRt a 4VR VLcos ωRt cos ωLt
a 2VRcos ωRt 6VRVL cos ωRt cos ωLt
a 8VR VLcos ωRt cos ωLt 8 VRVLcos ωRt cos ωLt
2a VRcos ωRt 2a VRVL cos ωR ωL t cos ωR ωL t a VR cos 3ωRt VRVLcos ωR 2ωL t VRVLcos ωR 2ωL t
VR cos ωRt a VRVLcos 3ωR ωL t VRVLcos 3ωR ωL t VRVL cos ωR 3ωL t VRVLcos ωR 3ωL t
3 VRVL VRVL cos ωR ωL t cos ωR ωL t
The IF output has the frequency component:
ωR， ωL， ωR ωL ， ωR 2ωL ， 3ωR ωL ， ωR 3ωL …
As can be seen that the even order harmonic of RF signal will be eliminated if RF input is placed at sum port of the single-balanced mixer.
Similarly, if the RF drive were in anti-phase and the LO in-phase, all spurious products with n even would be rejected. The anti-phase signal is also cancelled at the IF port, because the LO drive should be at a significantly higher level than the RF signal, it is often chosen as the anti-phase signal to increase the LO to IF isolation.
The RF short-circuit, shown at the IF port in Figure 4.1-1 is required for the mixer to work appropriately. If the RF impedance at the IF port were high, the RF signal voltage across the diodes would be small and the mixer's conversion loss would be very high. The LO signal, however, does not require a low impedance at the IF port. Because the LO is a balanced signal across the diode pair, the common port of the diodes is a virtual ground to the LO. The LO drive across the two diodes adds destructively to a null at the common port, as if it were grounded. In most cases, the LO and the RF are comparatively close in frequency, so the RF short circuit will also be a good LO short circuit.
The design procedure for a balanced diode mixer is similar to that for a single-ended. The only difference is that the balun structure providing the RF and LO isolation. As described in [11], which provide a technique to enhance the isolation performance of the rat race coupler. One option for the balun realization is a rat-race coupler. This is a very popular option at microwave frequencies where it is a comparatively small structure that can be produced inexpensively on a printed substrate.
4.2 Circuit design
The rat race ring is a widely used 180o hybrid coupler. Its drawbacks are its large size and limited bandwidth. The limiting factor in the hybrid ring coupler is the three-quarter wavelength section, which restricts the useful frequency range for the 180°
hybrid to f0 ± 0.23f0 where f0 is the center frequency in the band of interest . Numerous publications have been produced to improve the performance of this type of coupler.
Several design techniques have been proposed to enhance the useful bandwidth and to reduce its size. In [12] one quarter wavelength section with phase reversal was used to replace the three-quarter wavelength line. This phase-reversal section was realized with parallel coupled lines with two diagonal grounded ends (show in figure 4.2-1). Such a modified coupler achieved more than one-octave bandwidth. Although the bandwidth increases considerably, the even-mode impedance required for the coupled section would be too large to be realized, which is difficult to fabricate by using conventional chemical etching technique.
Figure 4.2-1 March's version of rat-race coupler
The conventional rat-race hybrids are inherently narrowband structures. This bandwidth limitation was attributed to the narrowband phase inverter within the quarter-wavelength and
3/4–wavelength line section. Many efforts have been made to make the bandwidth of rat-race ring coupler larger [13][14]. Most of them pay their attention by making a broadband phase inverter.
The finite- ground-plane CPW (FCPW) is a good candidate to realize this ideal phase inverter, because the “hot” lines as well as the ground planes are located on the upper surface of the carrier material. This enables parallel implementation of active and passive lumped elements into the circuit without any via hole structure, which results in a significant simplification in manufacturing process.
Figure 4.2-2 Twist between signal and ground path
Even if an ideal phase inverter is used, the conventional rat-race ring coupler with 70.7Ω ring impedance and Butterworth-type response is still limited to of about 74%
fractional bandwidth for return loss better than 15 dB. The ring coupler contain an ideal phase inverter can show a Chebyshev-type response of order two. For 12 dB return loss, the ring coupler with 55Ω ring impedance has 100% fractional bandwidth.
Because of the crossover at the ring arm, the signal line of the rat-race ring is DC grounded. We must use RF virtual ground to terminate two diodes and the IF signals are picked up from these RF virtue ground. The design parameters and circuit dimensions are list in Table 4.2-1.
Table 4.2 Design parameters and circuit dimensions of the rat-race ring
This single-balanced mixer is fabricated on 15mil Al2O3 substrate with center frequency 4GHz and 100% fractional bandwidth. The RF virtual ground can be formed by an FCPW open stub or shunt a capacitor. Here we used a 2pF capacitor at the IF port.
The diodes used in the mixer are Metelics silicon schottky diodes (MSS30,242-B20). In view of the layout of the IQ mixer, we squeeze the single-balanced mixer. The effect of the bond wires at crossover can be compensated by shortening the corresponding ring arms about 5 mils.
4.3 Measurement
There are two ways to excite the single-balanced mixer. One is to excite Local source at sum port and the other is to excite it at difference port. The measurement results are shown in the following figures respectively.
Figure 4.3-1 Conversion loss versus RF frequency. ( Local at difference port )
Figure 4.3-2 LO to RF isolation and RF to IF isolation ( Local at difference port )
Figure 4.3-3 Conversion loss versus IF frequency for fixed LO frequency.
( Local at difference port )
Figure 4.3-4 Conversion loss versus LO power
Figure 4.3-5 P1dB ( Local at difference port )
Figure 4.3-6 Conversion loss versus RF frequency. ( Local at sum port )
Figure 4.3-7 LO to RF isolation and RF to IF isolation ( Local at sum port )
Figure 4.3-8 Conversion loss versus IF frequency for fixed LO frequency.
( Local at sum port )
The conversion loss is around 8dB over the desired RF frequency band and it’s better when RF signal is excited at difference port. In this case, RF signal is virtual ground at IF port that causes the voltage across the diodes would be larger, hence the conversion loss would be smaller.
The RF to LO isolation is provided by the ring because RF port is also the virtual ground of the LO signal and vice versa. From figure 4.3-2, the RF to IF isolation is poor compared with figure 4.3-6. Because RF and IF are both placed at sum port, the ring provides no inherent isolation. The isolation here is only provided by a 2pF shunt capacitor. One way to solve this problem is to use a sharp low pass filter rather than just one order at IF port. From figure 4.3-6, the RF to IF isolation is better when RF is placed at difference port because the IF port is the virtual ground of the RF signal and the effect of the capacitor (RF-short circuit) The photograph of the circuit is shown in figure 4.3-8.
Figure 4.3-9 photograph of the proposed single-balanced mixer
Chapter 5 I/Q mixer
In this chapter, three device ( coupler, power divider, single-balanced mixer) are constituted to form the I/Q mixer. The whole circuit is fabricated in a one inch by one inch Al2O3 substrate. The measurement result will display in the following section. The photograph of the circuit is shown in figure 5-1.
Figure 5-1 The photograph of the I/Q mixer
5.1 Measurement
Figure 5.1-1 shows the conversion loss versus RF frequency. The conversion loss at the desired frequency band is around 12dB. The CH1 and CH2 are the outputs of the I/Q mixer which is shown in figure 5-1.
Figure 5.1-1 Conversion loss versus RF frequency ( LO (11dBm) is excited from 90 degree hybrid and RF (0dBm) is excited from the power divider )
Figure 5.1-2 shows the conversion loss versus RF frequency The conversion at the desired frequency band is around 12dB too.
Figure 5.1-2 Conversion loss versus RF frequency ( LO (11dBm) is excited from the
power divider hybrid and RF (0dBm) is excited from 90 degree hybrid )
Figure 5.1-3 Conversion loss versus LO power ( LO from 90o hybrid ; RF from power divider ;IF=5 MHz ; RF<LO )
There are two methods to check that the two outputs of the I/Q mixer have 90 degree phase difference. First, we can just excite the desired RF and LO signal in a fixed frequency and see the result. If LO is 2GHz and RF is 1995MHz. Two outputs of the I/Q mixer is shown in figure 5.1-4.
Figure 5.1-4 LO = 2GHz; RF = 1995 MHz ; IF = 5 MHz
As can be seen the two outputs has a phase difference 90 degree. The following figures show the results with different LO and RF frequency.
Figure 5.1-5 LO = 3GHz; RF = 2995 MHz ; IF = 5 MHz
Figure 5.1-6 LO = 4GHz; RF = 3995 MHz ; IF = 5 MHz
Figure 5.1-7 LO = 5GHz; RF = 4995 MHz ; IF = 5 MHz
Figure 5.1-8 LO = 6GHz; RF = 5995 MHz ; IF = 5 MHz
The second method can be shown in figure 5.1-9.
Figure 5.1-9 Second method to check the phase difference between two outputs of I/Q mixer
The RF and LO of the I/Q mixer is excited by a signal which its frequency change with time. The two outputs will produce DC voltage (cosθ , sinθ) because RF frequency is equal to LO frequency. The delay line in the upper path is essential for this method, because it introduce a phase delay. The phase delay is changed with frequency of the input signal because a same delay line saw different electric length at different frequency. Hence the DC outputs will also change with time. Figure 5.1-10 show the measurement result of second method.
Figure 5.1-10 Measurement result of second method.
The difference between the first method and the second method is that the first method can only see the phase difference and amplitude balance at some fixed frequency. The second method can see the results over all frequency components.
Chapter 6 Conclusion
This thesis has demonstrated a minimized wideband I/Q mixer on a one inch by one inch Al O substrate with a dielectric constant of 9.8.
In chapter 2, miniaturized wideband quadrature hybrid coupler has been realized by using three-section cascaded CPW coupler structure. The return loss would be better if the meander ground in the center section is used. The way to tune the meander ground is to let the input impedance around 50Ω, because the deep in the input impedance diagram can change if the dimension of the meander is changed. In consider of the area limitation, the length of the coupler is shrinked and the center frequency is shifted to higher frequency.
In chapter 3, a wideband wilkinson power divider is fabricated. Because the circuit is in CPW based, the coupling between two paths can be reduce by insert a ground strip between them. Hence, the circuit size is reduced.
In chapter 4, a single-balanced mixer is fabricated. The 180 degree hybrid in the mixer is chosen as a rat race ring coupler. To realized a wideband rat race ring, we can replace the 3/4 wavelength transmission line by a 1/4 wavelength transmission and a phase inverter which not only widen the bandwidth but also reduce the circuit size. To further reduce the circuit size, the diodes is placed inside the ring and the RF virtual ground is form by a shunt 2pF capacitor.
In chapter 5, the circuits fabricated in previous chapter are combined to form an I/Q mixer. There are two ways to check the phase and magnitude difference between two outputs of I/Q mixer. The measurement result is shown in figures and the specification is achieved.
References
[1]E. G. Cristal and L. Young, “Theory and tables of optimum symmetrical TEM-Mode coupled transmission line directional couplers,” IEEE Trans. Microwave Theory Tech., vol. MTT-13, no. 5, pp. 544–558, Sep. 1965
[2]J. S. Izadian, “A new 6–18 GHz, 3dB multi-section hybrid coupler using asymmetric broadside, and edge coupled lines,” in IEEE MTT-S Int. Microwave Symp. Dig., 1989, pp. 243–246.
[3] G. Kemp, J. Hobdell, and J. W. Biggin, “Ultra-wideband quadrature coupler,”
Electron. Lett., vol. 19, no. 6, pp. 197–198, 1983.
[4] S. Uysal and H. Aghvami, “Synthesis, design, and construction of ultra-wide-band
[4] S. Uysal and H. Aghvami, “Synthesis, design, and construction of ultra-wide-band