Modelling of a Printed VHF Balun Using E-M Simulation Techniques

Home , Balun, Inductive coupling, Leakage inductance

ARMMS Conference April 2013 Powerful Microwave Dominic FitzPatrick

Dominic FitzPatrick PoweRFul Microwave 15 Adelaide Place, Ryde Isle of Wight, PO33 3DP, UK [email protected]

Abstract —this paper describes a design approach for printed the advent of higher thermal conductivity substrates. Indeed Baluns. One route to high efficiency amplifiers is to construct a [1] itself demonstrates a planar combiner for a 1.1kW balanced design where two transistors are driven 180° out of amplifier, Figure 1. phase. Structures that can create these phase shifts are called The advantages from a high power amplifier point of Baluns, BALanced to UNbalanced. Commonly these are view of a balanced (or push-pull) design are significant: constructed from coaxial cables, often incorporating ferrites; • High efficiency an alternative approach using planar transmission lines has • 4x increase in device impedance compared to a cost and assembly advantages but has suffered from being single ended circuit. difficult to design, partly due to a lack of adequate linear • models. Modern E-M simulations which can create an E-M Excellent even harmonic rejection. simulation from a conventionally described microstrip circuit • Impedance transformation. can be utilised to accurately analyse such structures. • Increased reproducibility and lower assembly costs. Keywords – Balun, balanced amplifiers, push-pull, VHF power combiners, power dividers, suspended stripline, E-M CAD.

I. INTRODUCTION At microwave frequencies (>1GHz) the use of printed microstrip couplers has been well established and numerous papers have been written about the design of such structures. Thus it came as something of a surprise when asked to update the design of a VHF power amplifier that little had been written about the subject of printed Baluns. Perhaps even more surprising was that the predominant approach to power combining at these frequencies used coaxial cables with inherent assembly, cost and thermal issues, Figure 2. Figure 1, NXP DVB-T amplifier using planar combiners [1]. There is some debate as to which approach is better at power handling; a useful reference on the subject [1] states that “planar structures are not able to handle as much average II. PLANAR COUPLER THEORY power as broadband transmission line transformers…”. It is A common error is to forget that the planar balun is not not entirely clear to the author why this should be the case, if dependent on fractions of a wavelength, but rather relies on good thermal design practice is followed and especially with inductive coupling. The theory of the coupling is complex and one approach to modelling it is to use superposition principles, as has been described in detail [2]. It is beneficial to recall the basics of the ideal transformer behaviour in order to start to formulate a design method for planar couplers. In the ideal transformer two separate wires are coiled around a former whereby the flow of current through the one wire (the primary) causes electric and magnetic fields which interact with the other wire (the secondary) to cause a current to flow in this wire. In the ideal transformer it is assumed that: a) The magnetic flux is the same for both coils (there is no flux leakage. Figure 2, Freescale 1100W FM Broadcast Reference Design

Modelling of a Printed VHF Balun Using E-M Simulation Techniques 1 ARMMS Conference April 2013 Powerful Microwave Dominic FitzPatrick

b) Faradays electro-motive law applies: the voltage induced is proportional to the rate of change of PORT INDK current times the number of turns. P=1 ID=L2 c) That there are no losses, i.e. the source and load Z=50 Ohm L=57.74 nH power are the same. 1 2 d) That the permeability of the ideal transformer is K independent of flux density, i.e. it is a linear device.

Further it can be shown, [3] that the ratio of the source and L1 L2 load impedance is proportional to the square of the turns INDM ratio. This is important as it highlights the second function of ID=M1 the balun, that of an impedance transformer. M=39.45 nH K In practice however: i. There is flux leakage, which is represented by leakage inductance. ZL=7.5 ii. The magnetising inductance is finite. K iii. There are copper and core (hysteresis and eddy 2 1 currents) losses. PORT INDK PORT iv. The relative permeability of magnetic materials P=3 ID=L1 P=2 does change with DC and RF currents (and Z=ZL Ohm L=45.5 nH Z=ZL Ohm frequency and temperature). Figure 3, Circuit Model of Mutually Coupled Inductor Balun v. There is parasitics capacitance between coil windings. Insertion and Return IP Matched Coupler Coils 0 0 The coupling between the two coils is described in terms of m2 the mutual inductance, , and this in turn can be used to -2 DB(|S(2,1)|) (L) -6 M m1 Coupling Port 2 calculated the coupling coefficient, K, as described in {1}, DB(|S(1,1)|) (R) and the relationship between secondary inductance LS and -4 I/P Match -12 the other key parameters are given in {3}, for a full DB(|S(2,2)|) (R) derivation see [3]. The subscript “S” can be confusing for in -6 O/P Match -18

m1: 98 MHz Loss (dB) Return the case of Z and R it refers to ‘source’ and L it refers to Loss Insertion (dB) S S S -3.01 dB secondary. These relationships can be modelled using a -8 m2: 98 MHz -24 linear simulator as shown in Figure 3. -6.03 dB -10 -30 20 45 70 95 120 145 170 195 220 = {1} Frequency (MHz) × Figure 4, Narrow band response of capacitively tuned input. {2} = = Output Phase Performance {3} 90 190 = × In order to match the inductance of the input of the 0 186 transformer a shunt capacitor is added. This resonates with the inductance of the primary to give a good, if narrow band -90 182 match, as shown in Figure 4. The phase difference between -180 178 the output ports remains a constant 180° in both the matched Phase (deg) and unmatched case although the actual phase trajectory Phase Difference (deg) changes, Figure 5. The anti-phase performance is intuitive, -270 174 the current flowing in the two output ports being in opposite directions. The impact of the input resonating capacitor can -360 170 20 70 120 170 220 270 300 probably best be seen by looking at the changes to the Frequency (MHz) impedances on a Smith Chart, Figure 6. The dashed lines Port 2 Phase Shift Matched (L, Deg) Phase Difference Matched (R, Deg) Port 3 Phase Shift UnMatched (L, Deg) shows the impedances of the purely inductive coupled coils Port 3 Phase Shift Matched (L, Deg) Port 2 Phase Shift UnMatched (L, Deg) Phase Difference UnMatched (R, Deg) and for reference the solid red line along the perimeter of the Figure 5, 180° phase differential between Balun ports chart is an inductor of the same value as the primary.

Modelling of a Printed VHF Balun Using E-M Simulation Techniques 2 ARMMS Conference April 2013 Powerful Microwave Dominic FitzPatrick

match. This second capacitor not only ‘tightens’ the Coupled Coil Impedances

98 MHz resonance at the output ports, but also introduces an 8 Swp Max

1.0 .

r -0.0 Ohm 0 300MHz inflection in the input impedance trajectory, which broadens

6 x 35.5 Ohm .

0 0 the input match, Figure 7. An attractive part of this approach . 2 98 MHz

r 102.3 Ohm is that the parasitic capacitance of an amplifier’s port 4 .

0 98 MHz x 149.60 Ohm r 8.8 Ohm 3. impedance can be absorbed into this resonating capacitor. 0 x 19.2 Ohm 4. The next stage in the design process is to attempt to

2 . realise these coupled inductances in suspended stripline. 0 The problem then comes translating these values into ‘real’ 0.0 1 circuit values, i.e. the width and length of the tracks and the impact of the substrate thickness and dielectric. It is not 0 0.2 0.4 0.6 0.8 1.0 2.0 3.0 4.0 5.0 10.0

clear what coupling factor, K, one will get in practice at the

0 . 0 1 outset (it can be calculated retrospectively). The authors of - [1] found the mathematical approaches impractical and so

0. - 0

98 MHz 98 MHz .

- settled for an iterative approach using 3D E-M analysis

r 149.70 Ohm r 50.7 Ohm . 4

x 0.1 Ohm x 1.4 Ohm - approach.

3 4 - .

Inductor Capacitively Matched. I/P

6 2 - III. SUSPENDED STRIPLINE IMPLEMENTATION . 0 - Input Port 8 O/P with I/P capacitor . Swp Min 0

- In its most basic implementation the printed balun Output Port -1.0 10MHz consists of two tracks printed on opposite sides of a printed Figure 6, impedance of purely inductive coupled inductors SBCPL (dashed) and effect of resonating input capacitor. ID=TL1 W1=0.3 mm W2=1.81 mm The mutual inductance, secondary and lower load L=70 mm impedances reduce the effective reactance of the primary PORT Offs=0 mm SSUBT P=1 Acc=1 Er1=1 coil. The effect of the resonating capacitor matches the Er2=3.25 Z=50 Ohm TSwitch=T2=-T1 3 primary at the fundamental frequency. Er3=1 The bandwidth can be improved by the addition of W1 Tand1=0.0 Tand2=0.0025 capacitance on the output ports; if this is tuned to a slightly Tand3=0 H1=5 mm different frequency to that at the input, then the effective 2 4 H2=0.27 mm bandwidth can be extended. However nothing in this life is W2 H3=5 mm free and the cost of this bandwidth is a reduction in input T=0.018 mm CAP PORT CAP PORT Rho=1 ID=C1 P=2 ID=C2 P=3 Name=SSUBT1 Capacitively Tuned Coupled Coils C=67 pF Z=7.5 Ohm C=83 pF Z=7.5 Ohm

8 Swp Max

1.0 .

0 300MHz

. 98 MHz 0 0 . r 139.3 Ohm 2

x -6.9 Ohm 4

. 0 0 3.

0 4.

5.0 Figure 8, Simple planar balun transformer.

2 . 0

10.0 circuit board. This is easily and quickly analysed [4] in MWO using the circuit as shown in Figure 8. This model 10.0 0 0.2 0.4 0.6 0.8 1.0 2.0 3.0 4.0 5.0 provides a quick and useful starting point, as it can be 98 MHz

r 43.9 Ohm quickly optimised and gives values for the line widths as

0 .

0 1 x -1.5 Ohm - well as giving an assessment of the impact of different

2 substrate materials and thicknesses. However there are

- 0 . 5

- drawbacks. The model assumes that the tracks follow the

0 . 4

- same paths on opposite sides of the board (although they can

3 4 - . be offset), and there are no models for bends so the layout is 0

0 not practical. If we look at the balun implemented in [1] we

S(1,1) .

2 6 - . 0 can see that the underside track is a spiral whilst that on the -

S(2,2) 8 . Swp Min 0 top is a dimple ‘C’ shape, Figure 9. In this case the - S(3,3) -1.0 10MHz unbalanced signal enters (or leaves) the spiral inductor on the Figure 7, Impedance trajectories after capacitive tuning at lower out end and the grounded end is connected through via input and output. holes to the ‘virtual’ ground at the mid-point of the upper

Modelling of a Printed VHF Balun Using E-M Simulation Techniques 3 ARMMS Conference April 2013 Powerful Microwave Dominic FitzPatrick

It is clear that there are a number of options that we could take depending on how great an impedance transform we would wish to achieve with the balun. Note that we have only assumed a single frequency in the calculation and that the wider the bandwidth the larger will be the variation in K. As a general rule, for wider bandwidths we would attempt a lower impedance transformation, in order to minimise ripple. High Z ratios ~10 can be achieved is loss is not a critical factor, however particularly in power amplifiers it is unlikely that one would try to achieve more than a 5:1 transformation. In this example therefore we might select a value for n of 4, which still makes the job of matching to 2.5 Ω from 12.5 Ω challenging, (but not nearly as difficult as from 50 Ω). Table 1, provides starting values, which can be ‘plugged into the equivalent circuit model, Figure 3, and then Figure 9, 3-D drawing of balun from [1]. optimised for the required bandwidth. This then provides the template for optimising the simple balun, Figure 8, against. It trace. The space above and below the balun typically to >5x may be possible to include variables such as substrate the substrate thickness, should be air of dielectrically filled, thickness and dielectric constant, although these may be but a ground post could have been brought up into the centre. determined by other factors, for example the line widths for Alternatively the outer end could have been grounded and matching, cost and availability. Higher thermal conductivity centre linked to the unbalanced port (e.g. via a jumper). RF substrates (flexible/soft) are becoming available, but with From the designers perspective the problem we have is that limited choice in dielectric constant. Also the load for the layout of structures the microstrip/stripline models are capacitance can be included as a variable, but the next stage the most convenient, whilst the accuracy comes from of matching will be needed to compensate for any remaining running an E-M simulation of a specifically defined reactance. structure. From the simple model values, the more complicated Fortunately the Axiem simulator from AWR allows the shape desired can be created, again using the line widths and best of both worlds, geometry can be defined using circuit lengths of the simple circuit as a starting point. Typically the models and the software uses these to create the shapes for a input line will have been optimised to a narrow width, whilst structure that can be analysed using the E-M engine. the output line will be much wider, as the inductance ratio will have been attempted to be achieved with the same IV. DESIGNING A PLANAR BALUN USING AXIEM length line. By making the two lengths different more The first stage is to use the look at the impedance that practical line widths can be used. you are trying to match to and separate the resistive and The shape and size of the single turn is easiest to define reactive components. It is not necessary to achieve the entire first. That of the spiral is more complicated and the line match with the balun, it may be advantageous to take it in lengths are best described in relation to one side of a turn stages, as the greater the impedance step the higher the Q and taken as a reference. In this way only one parameter need be the narrower the bandwidth. For example with a balun changed to alter all the others. If the impedance ratio chosen centred at 98MHz, used to input match a very high power is not too large a single turn may be sufficient. It is of course device such as the NXP BLF178, the resistive element is of necessary to consider the current handling of the tracks when the order of 2.5 Ω and the reactive –j6.8 Ω (equivalent to a deciding on the line width to use, thus for higher currents 240pF capacitor), Table 1 gives the possible balun inductor wider lines will need to be longer to achieve the required values. inductance. For a Z S of 50 Ω and a L S of 11nH (to resonate with C L of 240pF) Conventional microstrip models are used to define the for a K=0.8 geometry. The shapes that are associated with the E-M ZL n LP M CP analysis are defined and an E-M extraction block is added to 50 1 7.0 7.0 375.0 the schematic, as shown in Figure 11. Those elements such as the ports, ground connection and the MSUB not part of 25 2 14.1 9.9 187.5 the E-M analysis are in blue. The “Extract” block contains 12.5 4 28.1 14.1 93.8 the E-M analysis parameters such as the cell size, simulation 10 5 35.2 15.7 75.0 engine and which block defines the materials used. The “Stackup” parameter refers to a multiple substrate definition 8.3 6.0 42.4 17.3 62.3 element which allows different material layers to be used, 4 12.5 87.9 24.9 30.0 thus giving the user control of the normal substrate 2 25 175.8 35.2 15.0 parameters, conductor materials and also the air gaps. In the schematic both track patterns have been defined; Table 1, possible transformer parameters for different one of the element parameters select which side of the board impedance ratios. a particular section is on. It is essential to ensure that all of

Modelling of a Printed VHF Balun Using E-M Simulation Techniques 4 ARMMS Conference April 2013 Powerful Microwave Dominic FitzPatrick

MCURVE ID=TL2 MLIN MCURVE W=W1 mm ID=TL26 ID=TL10 ANG=90 Deg W=W1 mm W=W1 mm R={W1/2} mm L=L6 mm ANG=90 Deg MTRACE2 MCURVE MCURVE R={W1/2} mm ID=X8 ID=TL15 ID=TL22 W=W2 mm W=W2 mm W=W2 mm MLIN L=WL2 mm ANG=90 Deg ANG=90 Deg BType=2 W1: 1 L3=15 PORT ID=TL32 R={W2/2} mm R={W2/2} mm M=1 G: 0.8 P=2 W=4 mm L1: 1.4 L4=L2+W1+G Z=50 Ohm L=3 mm MLIN L2: 15 ID=TL29 L3: 15 L5=L3+W1+G W=W1 mm MBENDRWX L4: 16.8 L=L7 mm ID=MS1 W2=8 MLIN L5: 16.8 L6=L2+2*W1+2*G MLIN MLIN WL1=1 ID=TL1 L6: 18.6 ID=TL21 PORT W1=W2 mm ID=TL33 W2=4 mm W=W2 mm L7={L5+W1+G} W=W1 mm P=3 W=4 mm Z=50 Ohm WL2=9 L=WL2 mm L={L5-7} mm L=3 mm MBENDRWX L8=L6+1 ID=MS2 W1=4 mm W2=W2 mm MLIN ID=TL12 MCURVE MTRACE2 W=W1 mm ID=TL9 EXTRACT MCURVE ID=TL35 MCURVE L={L1+5} mm W=W1 mm ID=EX2 ID=TL24 W=W2 mm ID=TL4 ANG=90 Deg EM_Doc="EM_Extract_Doc_OP" W=W2 mm L=WL2 mm W=W2 mm R={W1/2} mm Name="EM_Extract_OP" ANG=90 Deg BType=2 ANG=90 Deg Simulator=AXIEM R={W2/2} mm M=1 R={W2/2} mm X_Cell_Size=0.2 mm Y_Cell_Size=0.2 mm STACKUP="SUB2" Override_Options=Yes MCURVE Hierarchy=On ID=TL3 MLIN MLIN PORT SweepVar_Names="" MSUB ID=TL23 ID=TL25 Er=3 W=W1 mm P=1 ANG=90 Deg W=W1 mm W=W1 mm Z=50 Ohm H=0.762 mm L=L8 mm L=3 mm T=0.07 mm R={W1/2} mm Rho=1 Tand=0.0025 ErNom=3 Name=MSUB1 Figure 11, Balun circuit schematic, with elements associated with E-M analysis highlighted. the sections are joined and for this reason it is useful to make In this case we have just shown the resonating capacitors, sure that dimensions are multiples of the grid spacing. In this Figure 12, but other matching elements could also have been case a single turn of both primary and secondary are used, included. and the layout is shown in Figure 10. Note that this does not The results of optimising the capacitor values for a 3dB include the capacitors or grounding method, these must be split are shown in Figure 13. As can be seen with this added as in a normal layout. construction there is an imbalance of 0.5dB between the The E-M section of the circuit is separated out for speed ports. There are a number of techniques that can be of analysis; when this part of the circuit does not change it employed to correct for this and their effects can be quickly does not get re-examined, thus saving time. Instead it is appreciated using this simulation. Care must be taken to included as a block and the other circuit elements included. maintain the 180° phase difference with any correction, as this is the fundamental requirement of the balun. The anti- phase response required is met as shown in Figure 14.

SUBCKT ZL=6.25 PORT ID=S1 PORT P=1 NET="Output Balun" P=2 Z=50 Ohm Z=ZL Ohm 1 2

3 CAP ID=C1 C=81.91 pF CAP PORT ID=C2 P=3 C=211.4 pF Z=ZL Ohm Figure 12, Top level analysis schematic with E-M block Figure 10, Layout of balun transformer. contained in a sub circuit.

Modelling of a Printed VHF Balun Using E-M Simulation Techniques 5 ARMMS Conference April 2013 Powerful Microwave Dominic FitzPatrick

Double Tuned Balun Split Double Tuned Balun Phase Response 0 0 200 0 DB(|S(2,1)|) (R) DB(|S(2,3)|) (L) DB(|S(3,1)|) (R) Port 2 Port 2-3 Port 3 195 108 MHz -45 88 MHz 180 Deg 190 181 Deg -90 m1 -5 m2 -3 185 -135

180 -180

175 -225 (deg) Phase Isolation (dB) Isolation -10 -6 Insertion Loss (dB) Loss Insertion

Phase Difference (deg) Difference Phase 170 -270 Port 2 (R, Deg) m1: 98 MHz m2: 98 MHz 165 Phase Difference (L, Deg) -315 -3 dB -3.46 dB Port 3 (R, Deg) -15 -9 160 -360 60 70 80 90 100 110 120 130 140 150 60 70 80 90 100 110 120 130 140 150 Frequency (MHz) Frequency (MHz)

Figure 13, Tuned Balun power split. Figure 14, Tuned Balun Phase Response.

Simulation time for this structure is less than 1 minute on method,” IEEE Transactions Microwave Theory a fairly standard laptop and therefore tuning and optimisation Techniques, vol. 42, pp. 1223-1228, July 1994. of the design is practical. Automatic optimisation is feasible; however (as with most optimisation routines) a close eye needs to be kept on the design to ensure that the layout stays with realisable parameters. By setting the elements to “auto- snap” and limiting the optimisation to varying dimensions by the grid layout size should restrict this problem.

V. CONCLUSION An approach has been demonstrated to both enhance the understanding and to enable the design of a useful balun construction that is suitable for volume, high power, VHF- UHF applications. The use of Axiem ™ E-M simulation engine from AWR has been found to be very useful in accurately creating suspended stripline layouts for which conventional linear circuit models do not exist.

VI. ACKNOWLEDGMENT Thanks go to Andy Wallace of AWR for his help in implementing the model in Microwave Office.

VII. BIBLIOGRAPHY

[1] NXP, “AN10858: 174 MHz to 230 MHz DVB-T power amplifier with the BLF578,” NXP, 2010. [2] D. Jaisson, “Planar Impedance Transformer,” Transactions on Microwave Theory and Techniques, vol. 47, no. 5, pp. 592-595, May 1999. [3] P. Abrie, “Chapter 5: Coupled Coils and Transformers,” in RF and Microwave Amplifiers and Oscillators , 2nd ed., Artech House, 2009. [4] M. Bazdar, A. Djordjevic, R. Harrington and T. Sarkar, “Evaluation of quasi-static matrix paramters for multicond uctor transmission lines using Galerkin's

Modelling of a Printed VHF Balun Using E-M Simulation Techniques 6