Phase Shifter Design Tutorial

1 of 1 Phase Shifter Design Tutorial Introduction Phase shifters are devices used to adjust transmission phase in a system, they can be fixed phase digital phase shifters or analogue variable types. Switched-Line Phase shifter These phase shifters are similar to their attenuator equivalent where two SPDT switches are used to switch two line lengths, one of which is X degrees longer in electrical length than the other. The circuit is shown in Figure 1. Vcontrol Line length Line length 1 Figure 1 Switched-line phase shifter. Line length has a longer electrical length than line length 1 so when switched in line will cause an in-line phase shift β(l -l 1 ). Required phase shift β ( l l ) 1 ω Where β Vp and Vp 1 ε eff Example Design a switched-line phase shifter with a.5 degree phase shift at 4GHz, on a substrate with a dielectric constant of 9.9. l β.5.5degrees.ω 0.39rad 360 @ 4GHz, λ air c f 3x10 4x10 8 9 0.075m λ g λ ε air eff 0.075 9.9 0.038m π β λ g l β λg. π 0.038 * 0.39 1.485x10 π 3 m 1.485mm So we design the micro-strip lines such that line length is 1.485mm longer than line length 1.

of 1 However, we have to be careful in our choice of line lengths so that we don t get lines lengths of 180 degrees (or multiples of 180 degrees) which, would then form a resonator when switched out of circuit. Loaded-Line Phase shifter For phase shifts of <45 degrees we can make use of loaded-line phase shifters as shown in. These phase shifters work by adding a shunt reactance to the micro-strip line (in the form of an inductor or capacitor) causing the incident signal to undergo a phase shift. (Note in micro-strip the reactive component can be formed by a micro-strip stub). OR -jb +jb Figure Switched-line phase shifter. A shunt susceptance inductive (-jb) or capacitive (+jb) is switched in across the line causing a phase shift on the incident signal. Let jb be the normalised susceptance (from shunt elemant) ie jb jb.zo -1 b -tan and insertion loss of phase shifter will be 10log 10 b 1 + (db) 4

3 of 1 Example Like the previous phase shifter we shall design for a phase shift of.5 degrees @4GHz. Rearrange above b -.tan b - 0.885 ie inductive susceptance Normalise back to 50ohms 0.885 * 50 41.4ohms XL L π.f 41.4 π.4x10 9 1.65nH With a resulting insertion loss of 10log 10 1+ ( 0.885) 4 0.68dB The disadvantage of these phase shifters, are that in order to large values of phase shift, high values of b are required thus increasing the insertion loss. 45-degree phase shift (b ) will incur an insertion loss of 3dB. Also as these phase shifters rely on reflecting signals their return losses are very poor. Modified loaded-line Phase shifter The return losses of loaded-line phase shifters can be greatly improved by having two shunt susceptances separated by 90 degrees. If these susceptances are switched in or out by Pin diodes then a switchable phase shifter can be made as below. The equivalent circuit is a transmission line with phase θe. 90 degree line -jb +jb +jb -jb Figure 3 Improved switched-line phase shifter using two shunt susceptances and a quarter-wave length of transmission line. This circuit has very good input/output return losses.

4 of 1 Equivalent phase length ϑ cos e 1 ( b) Also, Impedance of circuit Ze Zo 1- b So, b < 1 and Ze > Zo L N ω.b B C πf.n This time we have a 4GHz phase shifter where two switched states give susceptances of +10Ω and -10Ω, and we wish to know the resulting phase shift and equivalent line impedance. b b on off 10 / 50 (capacitive) 0. & - 10/50 (inductive) - 0. cosθ eon - b on - 0. θ eon 101.5 degrees cosθ eoff - b off 0. θ offn 78.46 degrees Differential phase shift 101.5-78.46 3 degrees Equivalent line impedance Zo 1- b 50 1-0. 51Ω L N ω.b 50 9 π.4x10.0. 9.9nH B C πf.n 0. 0.159pF 9 π 4x10.50 The ADS simulation shown in Figure 4 shows the switched line attenuator using a 90-degree micro-strip line designed for 4GHz. For one simulation the inductors are connected resulting in the plots shown in Figure 6 and the other simulation the capacitors are connected resulting in the plots shown in Figure 5.

5 of 1 MSub S-PARAMETERS S_Param SP1 Start3.0 GHz Stop5.0 GHz Step4 MHz MSUB MSub1 H0.65 mm Er9.6 Mur1 Cond1.0E+50 Hu1.0e+033 mm T0 mm TanD0 Rough0 mm Term Ter Nu Z50 Ohm C C1 C0.159 pf MLIN TL1 Subst"MSub1" W0.65 mm L7.4 mm L L1 L9.9 nh R L L L9.9 nh R C C C0.159 pf Term Term Num Z50 Ohm Figure 4 ADS simulation of the improved switched-line phase shifter given in the example. In this case the inductors have been de-activated to leave the capacitors in circuit resulting in a phase shift of 101.5 degrees.

6 of 1-70 freq3.996ghz phase(s(,1))-10.95 phase(s(,1)) -80-90 -100-110 -10 0.0-0.1-130 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 m -10-0 db(s(,1)) -0.3 db(s(1,1)) -30-40 -50-60 -0.5 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 m freq3.996ghz db(s(,1))-0.006-70 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 freq4.000ghz db(s(1,1))-57.989 Figure 5 Improved switched-line phase shifter with capacitors switched in circuit. -50 freq3.996ghz phase(s(,1))-79.747 phase(s(,1)) -60-70 -80-90 -100 0.0-0.1-110 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 m -10-0 db(s(,1)) -0.3 db(s(1,1)) -30-40 -50-60 -0.5 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 m freq3.996ghz db(s(,1))-0.008-70 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 freq4.000ghz db(s(1,1))-40.955 Figure 6 Improved switched-line phase shifter with inductors switched in circuit.

7 of 1 Reflection Phase shifter Reflection phase shifters work by having switchable terminations which, create switchable reflection coefficients. The main type of reflection phase shifter uses switched line lengths either by using a PIN switch or by a variable reactance (eg varactor) to alter electrical length. In both cases the signal incurs twice the extra electrical length as the signal is reflected back. Switched Line reflection phase shifter The simplest example is to use a 90-degree hybrid (eg Lange or Rat-race) and two PIN diodes to either short to ground bypassing line length or switched out thus adding line length and adding a longer path for the signal to travel. The schematic of the circuit is shown in Figure 7. 90 degree hybrid coupler Line length 1 Line length 1 Line length / Line length / Figure 7 Reflection phase shifter using two PIN diodes to switch in or out the additional line lengths. Γ ON e jφ Γ OFF e j( φ+ ) For best operation Γ ON Γ * OFF ie Γ ON e -j( φ+ ) Giving : φ - φ φ kπ ( φ + ) + kπ kπ, where k 0,1,,3...

8 of 1 Example Switched line reflection phase shifter to give 45 degrees phase shift at 8GHz. Lange coupler length will be ~4mm long. Γ ON Γ φ o 1 Γ OFF Γ φ o φ φ 45 1 For best return loss performance Γ ON Γ * OFF φ1 kπ If k 0 then 45 φ1 -.5 degrees φ φ 45 1 + φ φ 45.5.5 degrees The ADS simulation for this circuit is shown in MSub S-PARAMETERS S_Param SP1 Start7.0 GHz Stop9.0 GHz Step4 MHz Term Ter Nu Z50 Ohm MLIN TL3 Subst"MSub1" W0.65 mm L0.91 mm MLIN TL1 Subst"MSub1" W0.65 mm L0.91 mm MLANG Lang1 Subst"MSub1" W0.05 mm S0.05 mm L3.9 mm MSUB MSub1 H0.65 mm Er9.6 Mur1 Cond1.0E+50 Hu1.0e+033 mm T0 mm TanD0.001 Rough0 mm MLIN TL Subst"MSub1" W0.65 mm L0.91 mm MLIN TL4 Subst"MSub1" W0.65 mm L0.1 mm Term Term Num Z50 Ohm Figure 8 ADS simulation of the switched line reflection phase shifter given in the example. In this case we are simulating the PIN diodes on and shorted to ground by the two ground points at the end of.5 degree micro-strip lines TL1 and TL. The resulting simulation of this circuit is shown in Figure 9. The other case is with the grounds disabled simulating the PINs switched off and the signal having to travel additionally along TL3 & TL4 (and of course back again). The resulting simulation of this is shown in

9 of 1 70 freq8.000ghz phase(s(,1))47.133 phase(s(,1)) 60 50 40 30-0.0 0 7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0 m -0 db(s(,1)) -0.03-0.04-0.05 m freq7.99ghz db(s(,1))-0.03 db(s(1,1)) - -4-6 freq8.004ghz db(s(1,1))-6.405-0.06 7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0-8 7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0 Figure 9 Resulting simulation from the circuit shown in Figure 8 with the diodes switched on shorting to ground and effectively switching out TL3 & TL4. 40 freq8.000ghz phase(s(,1))-1.68 phase(s(,1)) 0 0-0 db(s(,1)) -0.04-0.05-0.06-0.07-0.08-40 m m freq7.99ghz db(s(,1))-0.049 7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0 db(s(1,1)) -18-19 -0-1 freq8.004ghz db(s(1,1))-1.355-0.09 7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0-7.0 7. 7.4 7.6 7.8 8.0 8. 8.4 8.6 8.8 9.0 Figure 10 Resulting simulation from the circuit shown in Figure 8 with the diodes switched off (by disabling the grounds at the end of TL1 & TL) adding TL3 & TL4 transmission lines.

10 of 1 As can be seen there is approximately a 45 degree phase shift (the accuracy of this depends on the Lange coupler dimensions). Variable reactance reflection phase shifter This circuit again uses a 90-degree hybrid but instead of switched line lengths variable reactances are used. A variable reactance is in effect a variable electrical length therefore, using a variable reactance such as a varactor we can form a variable phase shifter. The schematic of the variable reactance reflection phase shifter is shown in Figure 11. 90 degree hybrid coupler Vbias Varctor 1 Varctor Vbias If you require a negative bias on the varactor then use another bias circuit here, and replace DC short circuit with a RF short circuit eg stub Figure 11 Variable reactance reflection phase shifter, using varactors as the variable reactance. Each varactor is bias via a choke with the same bias. There may be a requirement to use a varactor reference instead of 0V (caused by the DC ground). In this situation the DC ground is replaced by a RF short eg a quarter-wave capacitive stub and another bias circuit added. For example calculate the phase shift of a 4GHz variable reactance reflection phase shifter using Macom varactors type MA464.

11 of 1 The MA464 has a capacitance range of 0.6pF to 6pF (0V to 0.1V). The electrical length needs to be calculated for each capacitor value remembering that the phase is doubled due to the signal reflecting back from the short circuit on the other end of the varactor. From the Micro-strip tutorial we found the following relationship for a shunt capacitor:- Capacitor C Micro-strip Zo θ tanθ ωc Zo Where θ < 90 0 90 0 λ op 4 (1) Capacitor set to 6pF (ie Control voltage of 0V) Rearrange ωc tanφ Zo -1 9-1 o ( ω.c.zo) * tan ( π.4x10.6x10.50) 164-1 φ 6pF * tan () Capacitor set to 0.6pF (ie Control voltage of 0V) φ 0.6pF * tan -1-1 9-1 ( ω.c.zo) * tan ( π.4x10.0.6x10.50) 74 o Therefore, φ 6pF φ 0.6pF 164-74 90 degrees The ADS simulation in Figure 1 was initially run with the varactors set to 6pF and the PhaseShift element was then set to give 0 degree phase shift at 4GHz to set a reference. The simulation was then run again this time with the varactors set to 0.6pF resulting in the plots shown in Figure 13.

1 of 1 S-PARAMETERS S_Param SP1 Start3.0 GHz Stop5.0 GHz Step4 MHz Term Ter Nu Z50 Ohm C C1 C.6 pf MLANG Lang1 Subst"MSub1" W0.05 mm S0.05 mm L7.8 mm MSub MSUB MSub1 H0.65 mm Er9.6 Mur1 Cond1.0E+50 Hu1.0e+033 mm T0 mm TanD0.001 Rough0 mm PhaseShiftSML PS1 Phase-109.78 ZRef50. Ohm C C C.6 pf Term Term Num Z50 Ohm Figure 1 Variable reactance reflection phase shifter. The phase shift was set to give zero phase shift with the varactors set to 6pF (0V) as a reference, then the simulation was run again this time setting the varactors to 0.6pF (0V). The result of the second simulation is shown in Figure 13. 140 phase(s(,1)) 10 100 80 60 40 freq4.000ghz phase(s(,1))86.568 3.0 3. 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 Figure 13 Simulation from ADS schematic shown in Figure 1, with capacitors now set to 0.6pF (from 6pF) to show that maximum phase shift available if using the MaCOM MA46473 diodes.

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