The use of differential (or balanced) digital and analog circuits for information processing has increased in recent years . When transmitting high-speed electrical signals, both the electromagnetic (EM) fields generated by the transmitted signals and the ground plane return current might cause electrical interference on adjacent circuits. Moreover, with the trend of digital systems to move to lower operating voltage, logic signal swing and noise margin also decrease, thus deteriorating the noise immunity of the digital system.
Due to these and other reasons, differential signaling is becoming more and more popular in both digital and analog applications. Indeed, several common low-voltage communication standards (such as USB, Serial ATA or HDMI, among others) make use of differential signals. Note that, for the same operating voltage level, differential signals provide much lower return current on the ground plane, better immunity to noise, less electromagnetic interference (EMI) and less cross-talk when compared with conventional single-ended implementations. Also differential signals are not affected by external noise, which mainly couples to the common mode component of the total voltage.
However, although ideal differential signals are supposed to solve all the above-mentioned problems, in a realistic scenario, where the circuit symmetry has been slightly broken or the applied signals present some level of time skew, the presence of common-mode (CM) noise is unavoidable. This CM noise is the source of most of the radiation and EMI problems. Hence, differential circuits should be designed in such a way that CM is rejected and, at the same time, the differential-mode (DM) signal is not perturbed, thus preserving its integrity within the frequency range of interest.
In this context, many microwave differential (or balanced) devices have been proposed in the literature, including common mode filters based on artificial differential lines, balanced bandpass filters, power dividers / combiners, diplexers and passive equalizers. Among the aforementioned balanced devices, common mode filters and balanced bandpass filters are, by far, the ones that have attracted more attention in the literature. However, much less research has been carried out in the area of microwave differential diplexers. Given the current trends towards multi- band systems, diplexers offer a very interesting solution to increase the compactness and to reduce the cost of RF front- ends.
Therefore, the design of balanced diplexers deserves more attention. To the authors’ knowledge, two different kind of diplexers with differential operation have been proposed in the literature: balun diplexers, and balanced diplexers.
Balun diplexers are composed of a single-ended input port and two balanced output ports (or vice versa). In a balanced diplexer both input and output channels are differential in nature (we will refer to this type of diplexers as Balanced-to-Balanced (B-B) diplexers). In all cases, the most common procedure to perform differential diplexing operation consists in the design of two different filters (single-ended or balanced) connected to a common input port (which, again, can be single-ended or balanced).
Good DM transmission properties, high channel-to-channel isolation and weak CM transmission are simultaneously required. Several techniques have been used to accomplish the aforementioned goals to a greater or lesser extent. For example, the balun diplexers in makes use of bandpass filters whose resonators have DM and CM resonance frequencies far apart from each other. The filters are connected to a common input by means of a T-junction, providing good DM and CM responses with high isolation.
However, this configuration presents an intricate geometry, which complicates the design process. This idea was extended to design a balun diplexer and a balanced diplexer whose resonators require ground connection through via holes. This feature introduces additional complexity in the design and manufacturing process. The same concept is used for the design of balanced diplexers, with the novelty of the introduction of transmission zeros (TZs) associated with the existence of mutual couplings between stub loaded in- put/output lines. Although DM selectivity and isolation are good, CM suppression is poor due to the extra coupling path provided by the input/output lines.
To solve this problem, the structure is modified by introducing shorted stubs along the resonators symmetry plane. The length of the stubs is adjusted so as to introduce a common mode TZ at the center frequency of each channel passband. The main drawback of this technique is, once again, the requirement of using via holes.
The use of hybrid microstrip/slot line resonators prevents CM transmission and allows for the design of balun and balanced diplexers with good DM performance and high isolation levels. However, in practical applications, ground planes without slots are preferred to reduce radiation losses and possible electromagnetic compatibility (EMC) issues. Very recently, the authors of this contribution have presented a B-B diplexer based on edge-coupled split ring resonators based filters.
This design provides both good DM and CM response with a very compact design, at the expense of being a complicated structure where a sophisticated excitation mechanism is required. Finally, two different B-B diplexers using Chebyshev responses are presented based on dual mode resonators with magnetic coupling and microstrip slotline coupling schemes.
Although good performance within the passbands is obtained for both DM and CM, the proposed structures exhibit a relatively large electrical size. In addition, rather poor channel isolation is observed, and the structure with magnetic coupling suffers from CM resonances in the out-of-band region, thusdegrading the CM performance in the upper frequency region of the spectrum. To end this section, it is worth mentioning that some works on balanced quad-band diplexers making use of the techniques mentioned above have recently been reported.
In a recent paper by some of the authors, it was demonstrated that the use of magnetically coupled open-loop or folded stepped-impedance resonators offers a very simple solution to implement single-band balanced bandpass filters with high CM suppression and excellent DM performance. The electric nature of the CM coupling ensures an inherently poor CM transmission when magnetic coupling is used to generate the differential response.
In the present paper two novel balanced diplexers are proposed which are based on open loop (prototype I) and FSIRs (prototype II) balanced single band bandpass filters. It will be shown how the use of a well known design methodology for coupled resonator filters makes it possible the fabrication of a compact and high-performance balanced diplexer by joining the two balanced filters to a common balanced input.
The paper isorganized as follows: in section II the first diplexer prototype, based on two second order coupled open-loop resonators bal- anced filters, is presented. The second prototype, based on a couple of fourth order coupled stepped-impedance resonators (FSIRs) balanced filters, is presented in section III. Finally, some conclusions are provided in section IV to summarize the advantages of the proposed approach.
II. PROTOTYPE I: BALANCED DIPLEXER BASED ON SECOND ORDER FILTERS
As it has been said in the introduction, the design of the B-B diplexers proposed in this contribution starts with the design of the two required balanced filters. Each filter is in dependently designed and connected to the same differential input port to obtain the differential diplexing operation. The layouts of the microstrip configurations used for the implementation of the filters composing the balanced diplexer prototype:
In what follows, the superscripts “l” and “u” denote the lower and upper DM passbands. Under DM operation, the symmetry plane, AAj, in Fig. 1 behaves as a virtual short circuit, thus forcing the coupling mechanism of this configuration to be mainly magnetic in nature. However, under CM operation AAj is a virtual open-circuit, which leads to electric coupling in this case.
As it was proven, these features make it possible to design balanced bandpass filters with good DM performance and an inherently strong CM rejection. This response is achieved because of the contrast between the achieved weak electric coupling (CM) and strong magnetic coupling (DM). Apart from strong CM suppression, high DM and CM isolation between channels is provided by the chosen solution. The design of the balanced filters in Fig. 1(a) and (b) can be easily carried out using the appropriate values of the coupling coefficients, M , and external quality factors, Qe, according to the method already explained. The values of M and Qe depend on the DM filter specifications through the following well known expressions:
where n is the filter order, ∆ is the fractional bandwidth and gj (j = 0, . . . , n + 1) are the low-pass prototype element values for the filter response to be implemented.
In the case at hand, two n = 2 Butterworth filters, with ∆l = ∆u = 7 %, and center frequencies f l = 2.5 GHz , f u = 3.5 GHz areintended to be designed. The values of the corresponding low-pass prototype elements are g0 = g3 = 1 and g1 = g2 = 1.4142. Using these parameters and the required bandwidth, the theoretical values for M1,2 and Qe (the same for both bands in this particular case) can be computed using (1) and (2). This results in M l = M1,2 = 0.049 and Ql e1 = Ql e2 = Qle = Qu e1 = Q u e2= Qu = 20.20. The dielectric constant of the chosen substrate is εr = 3.0, its thickness h = 1.016 mm and the loss tangent tan δ = 0.0022.
If the balanced filters designed in subsection II.A are connected to a common differential input port, balanced diplexing operation can be performed. The proposed layout is shown in Fig. 4, where a T-junction is used to connect coth filters. In this figure, Zlin and Zuin represent the input impedances of the lower and upper branches of the T-junction seen from the T-junction bifurcation. The key point when introducing the T-junction is that the external quality factors at the filter inputs must be those imposed by the design spec- ifications. The T-junction must be then designed to preserve the required external quality factors. This ensures low return loss level at both output channels (good signal matching). As it can be seen in Fig. 4, there are several dimensional parameters involved in the T-junction design. For simplicity, we have set the values of l0 = 1.8 mm, wt = 0.2 mm and st = 0. The lengths of the branch feeding lines, lu and ll, have been used as the adjustable parameters to fit the desired external quality factors. Fig. 5(a) shows the coupling structure with the T-junction used to calculate the external quality factors Qu and Ql by means of the procedure already reported in the document below.
Note that, in contrast with the procedure followed in subsection II.A, where Que and Qle are separately calculated, here we propose the simultaneous determination of the external quality factors. For such derivation, it has been considered that, at fl0d, the upper-band resonator in Fig. 5(a) acts as a reactive load at the input of the lower-band resonator and vice versa. This provides a real and complete characterization of the input external quality factors of both channels. The design curves showing the behavior of Qlue versus lu using ll as a parameter are depicted in Fig. 5(b). Although,
as expected, Que (Qle) exhibits a stronger dependence with lu (ll) than with ll (lu), for an accurate derivation of Que and Qle both lengths must be considered. From Fig. 5(b), the values required to fulfill Que = Qle =20.2 are ll = 2:36mm and lu = 1:96 mm.
In order to verify the validity of the method used to design the T-junction, Fig. 6 shows the simulated DM response of the diplexer for ll = 2:36mm by using lu as sweep parameter. From Fig. 6(b) it can be seen that the lower band is well-matched for any value of lu, whereas the upper band return loss is strongly dependent on lu. The calculated value lu = 1:96mm provides the best return loss for the upper passband. The port-to-port isolation, |Sdd 32 |, is depicted in Fig. 6(c). It can be seen that the dimensions of the T-junction barely affect the isolation level between the two channels. This level keeps better than 35 dB and with almost the same frequency response independently of lu. This is an expected result, due to the separation between the two passbands.
In Fig. 7 a similar study is carried out interchanging the roles of ll and lu (now lu = 1:96 mm). This figure shows that the value of ll = 2:36mm provides the best matching for both bands. Note that this parameter can also be used to control the precise location of a transmission zero (TZ) existing around 5 GHz, if an adequate tradeoff between the position of this TZ and the matching level is attained. This TZ appears at the frequency at which Zl in = 0.
At such frequency the signalwill see a short circuit thus flowing towards the branch of the T-junction feeding the lower band channel. Then a TZ will appear at the upper band channel. Finally, the results for |Sdd32| shown in Fig. 7(c) confirm our hypothesis of good isolation between ports 2 and 3,independently of the dimensions of the
In order to clarify the design process of the B-to-B diplexer proposed in this section, the following summary is given below:
- The isolated filters are designed following the standard procedure well detailed in references in the full document.
- A T-junction with some arbitrarily chosen dimensions (for wt, l0, ll, lu and st) is introduced.
- There are several geometrical parameters defining the T-junction layout. Only two of those parameters have to be tuned to optimize the matching of the diplexer ports, since there are only two electrical parameters (the lower- and upper-band external quality factors) to be adjusted. Therefore, only the lengths of the branch feeding lines (ll, lu) are used as adjustable parameters to fit the required external quality factors at the input ports of the filters. The remaining geometrical parameter sare not modified in this optimization process. This step ends the design of the proposed B-to-B diplexer.
A prototype of the balanced diplexer in Fig. 4 has been fabricated using a LPKF Protolaser S machine and measured using the Agilent PNA-E8363B ANA with a N4420B test-set extension (four ports system). The simulated and measured DM and CM responses are shown in Fig. 8(a-d), and a photograph of the fabricated device is shown in Fig. 9. According to the plots in Fig. 8(a-d), the agreement between simulations and measurements is very good. The measured DM lower and upper passbands are centered at 2.51 GHz and 3.57 GHz, with an insertion loss (IL) level at the center frequencies of 1.14 dB and 1.21 dB, respectively.
The experimental fractional bandwidth is, as required, 7 % for both passbands. The measuredDMisolation (Iso) is better than 40 dB for the lower frequency channel and better than 33 dB for the upper one. In addition, the measured CM rejection is better than 50 dB and 48 dB for the lower and upper-band channels, respectively.
Furthermore, concerning the out-of-band performance of the DM, a rejection better than 20 dB is appreciated over almost the whole frequency range up to 10 GHz (there is a transmission peak of about -15 dB at around 8.3 GHz). Concerning CM rejection, it is better than 15 dB in both channels until 10 GHz and better than 50 dB within the two differential pass bands, leading to a high level of CMRR (as it will be seen in the forthcoming comparison table).
Finally, CM and DM isolation are better than 30 dB until 10 GHz. This demonstrates that the diplexer provides a very good response not only within the differential passbands of both channels, but also in the out of band region, over a wide bandwidth, for all the relevant scattering parameters.
In order to illustrate the benefits of using magnetically oupled resonators for the design of balanced diplexers, a comparison with previous contributions is provided in Table
I. From the data included in this table, it can be concluded that the balanced diplexer proposed in this paper exhibits a very competitive combination of common mode rejection ratio (CMRR) and size. These advantageous features have been highlighted in the table. Regarding the rest of electrical parameters, the presented structure is also very competitive.
In addition, the structure is obtained by following a very simple design process, where no higher order filters or additional elements such as via-holes, defected ground tructures or lumped/distributed components are needed. In spite of the simplicity of the design, a very good performance has been achieved for the diplexer operation.
III. PROTOTYPE II: BALANCED DIPLEXER BASED ON FOURTH ORDER FILTERS
The low-order balanced diplexer studied in the previous section has been shown to be very effective to divide a differential signal into two different channels (with good
isolation between them) and, at the same time, to prevent CM transmission.
However, it would be quite interesting to test if our proposal is suitable to operate when the two differential outputs must handle signals which are closer to each other in the frequency domain. For this, better filter selectivity is required for both channels. To achieve this goal, extra coupling paths can be introduced in the structure.
This technique allows for the introduction of several TZs at the expense of degrading CM rejection (CM finds in the extra coupling paths an alternative way to pass through the system). Thus, in this paper, in order to improve filters selectivity, a different strategy will be followed: the employment of higher order filters.
Since the structures in this paper are very simple and the design procedure is well stablished, increasing the filters order is straightforward. Obviously, this will enhance filters selectivity. The layout of the new proposed diplexer (prototype II) is shown in Fig. 10. As in the previous example, the lower and upper frequency band channels are 330 and 220, respectively. Each filter involves two different resonators which have been denoted by subscripts “a” and “b”.
Comparing the layouts in Fig. 4 and Fig. 10, two important differences can be appreciated:
1.The filters in Fig. 10 are not capacitively excited but inductively excited. This is due to the fact that fourth order filters have two different coupling sections: an
electric coupling section (between resonators “a-b” separated by sl,u1 and a magnetic coupling section (between resonators “b-b” separated by sl,u2 ).
Since the excitation is carried out by the inductive region (strip of width wl,u1,a) of resonators “a”, inductive excitation is more effective and simpler than capacitive excitation, as discussed, for instance, in the full document. However, the presence of at least one section with magnetic coupling in each filter ensures strong CM rejection, as it will be demonstrated next.
2. The resonators used in Fig. 10 are FSIRs, instead of open-loop resonators. This has been done wih two main targets. The first one is to achieve compactness. Since the filters of the B-B diplexer in this section require the use of more resonators, the use of FSIRs allows for a reasonably compact design when compared with the one obtained using open-loop resonators.
Second, to demonstrate that the methodology used in the previous section can be employed with different kind of microstrip resonators. In this sense, the method is quite general, as discussed in the full document. After these considerations, we are now in a position to define the haracteristics of the differential passbands for the channels of the diplexer in Fig. 10: both filters will be of order n = 4, with Butterworth response, l = 15%, u = 10 %, and center frequencies fl0d = 2:49 GHz , fu0d = 2:98 GHz.
Note that the differential passband fractional band widths have been chosen to be different, in contrast with our previous example. According to (1) and (2), the equired values of the coupling coefficients and external quality factors result to be: (i) lower channel Ml1;2 = Ml3;4 = 0:13, Ml2;3 = 0:081, Qle1 = Qle4 = Qle = 5:10 and (ii) upper channel Mu1;2 = Mu3;4 = 0:084, Mu2;3 = 0:054, Que1 = Que4 = Que = 7:654.
The low-pass prototype element values for the calculation of the external quality factors and coupling coefficients are g0 = g5 = 1, g1 = g4 = 0:7654 and g2 = g3 = 1:8478. The same substrate used to design and fabricate the prototype I is employed in this design. Design curves similar to those in Fig. 2(a) and (b) can be plotted to extract the required values of Ml,ui;i+1 and Ql,ue . Such curves have not been included here in order to save some space and prevent writing a too long paper. Nevertheless, it is worth to clarify that Ml,u1;2 (Ml,u3;4) and Ml,u2;3 are controlled by Sl,u1 and Sl,u2 , respectively, while Ql,ue are controlled by tl,u, respectively.
Once the filters have been designed, both are connected to the common differential input 110 by means of a T-junction, whose branches are optimized in order to preserve the required external quality factors. Curves similar to those in Fig. 5 can be plotted in order to find the correct values of ll and lu, although they have not been included here for the sake of brevity. The final dimensions of the B-B diplexer presented in this section are shown in the caption of Fig. 10.
The diplexer in Fig. 10 has been simulated, fabricated and measured. The results are plotted in Fig. 11, where good agreement between simulations and measurements is found. The measured center frequencies (DM) and FBWs result to be fl0d = 2:49 GHz, fu0d = 2:98 GHz, l = 15%,u = 10 %, respectively. The measured IL at the center frequencies is 1.15 dB (lower channel) and 1.54 dB (upper channel).
When compared with the response in Fig. 8, channels roll-off is greater in this new design (better filters selectivity). DM isolation is well below 30 dB in the whole considered frequency range. Out-of-band rejection is also better than 30 dB practically until 10 GHz, except for a small transmission peak in channel 330 at about 9.1 GHz (still better than 20 dB). Regarding CM results, Fig. 11 reveals very strong rejection level in both channels (expected from magnetic coupling).
CM suppression is larger than 50 dB and 45 dB for the lower and upper band, respectively. Moreover, CM rejection is better than 30 dB in the whole frequency range for both channels, except for a ransmission peak of -15 dB in channel 220 at approximately 7 GHz. CM isolation is better than 40 dB until 10 GHz.
In brief, the proposed diplexer provides very good performance in terms of DM signal quality transmission and CM rejection. No interaction is observed between output channels notwithstanding the proximity between them. In order to demonstrate the benefits of the B-B diplexer within this section, it has been compared with other contributions in Table I. According to this table, the diplexer seems to be quite competitive in terms of CMRR, compactness (in spite of the order n = 4), and differential passbands proximity (our proposal provides the lowest value of fu0d=fl0d).
A photograph of the fabricated prototype is depicted in Fig. 12.
In this paper, two new balanced-to-balanced diplexers are presented in microstrip technology. Prototype I is composed of two balanced bandpass filters based on magnetically coupled open-loop resonators. Prototype II is based on two balanced bandpass filters designed using magnetically coupled stepped-impedade resonators. The design process in both cases is simple and straightforward. Basically, it consists in designing each filter independently, with their desired performances, and then joining them to the same differential input by means of a T-shaped connecting transmission line path. The length of each arm of the T-junction must be tuned to provide a good level of return loss in the two passbands.
Design curves can be generated from electromagnetic simulations taking into account the presence of the two resonators. This tuning process can be easily achieved with low computational cost. Measured results confirm the benefits of the proposed idea.
Finally, when compared with previous contributions, prototype I offers one of the highest level of compactness and common-mode rejection ratio, while still being very competitive in terms of the other relevant electrical parameters. Prototype II provides the lowest ratio between center frequencies while conserving a competitive compactness in spite of the high-order filters used in the design. Good roll-off is observed in each channel for this prototype without the need of using complex transfer functions.
This work has been supported in part by the Spanish Ministerio de Economía y Competitividad with European Union FEDER Funds (contracts TEC2013-41913-P, TEC2016-75650-R, and TEC2017-84724-P), by the Spanish Junta de Andalucía (project P12-TIC- 1435), and by Generalitat de Catalunya (contract 2014SGR-157).