04 Matching Networks. Dipl.-Ing. Dr. Michael Gebhart, MSc

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1 04 Matching Networks 4th unit in course 3, F Basics and omponents ipl.-ing. r. Michael Gebhart, Mc FI Qualification Network, University of pplied ciences, ampus W 013/14, eptember 30 th

2 ontent Introduction: How to match the chip output to the antenna impedance? - oop antenna - Quality factor - ow impedance or load matching: ower and Q - Modulation envelope and Q-requirement (single resonance) - Network transformation: differential to single-ended The general matching solution: π and T-topology networks Impedance adjustment with -topology - ntenna impedance - Q-factor adjustment for operating frequency - etermination of serial and parallel capacitance for impedance adjustment The resonant coupling system - How near-field coupling affects the air interface page

output. This allows optimum power transfer and to meet other contactless property requirements.

3 How to match the chip to the antenna? NF device in eader Mode (TX), a network adjusts (transforms) the antenna impedance to a desired value for the chip driver output. This allows optimum power transfer and to meet other contactless property requirements. NF hip Matching Network NF ntenna? chip output impedance antenna MHz e.g. 5 Ω e.g. 0.6 j 110 Ω conjugate reactance conjugate reactance Narrow-band matching for the MHz carrier frequency in reader mode page 3

4 oop antenna for ontactless ommunication The loop antenna is a distributed component with inductance () as main element and capacitance () and resistance () as parasitic network elements. End of coil turns tart of coil turns n n n For simulation it must be represented by an equivalent circuit network of lumped elements. Over a wide frequency range this can be a loose coupled reactive ladder network of resonance circuits - it has several resonances in frequency domain. t MHz carrier frequency we use the fundamental (lowest) resonance. o we can simplify the equivalent circuit e.g. to a parallel resonance circuit (since losses are mainly determined by chip current consumption in roximity ystems). Note: This is a narrow-band approximation only! page 4

The Quality factor Originally, the quality factor reports the quality at which the component (coil, capacitor) represents the pure network element (inductance, capacitance).

5 The Quality factor Originally, the quality factor reports the quality at which the component (coil, capacitor) represents the pure network element (inductance, capacitance). Q( ) Q ( ) esistance f f E MX Frequency For a nd order resonant circuit, Q can be determined in frequency domain. Q is related to the bandwidth and can be measured from the esistance trace. Note: This is only valid, if the broad E Q( ) band equivalent circuit f representation really is a parallel resonant circuit! For a nd order resonant circuit, Q can also be determined in time domain. Q is related to the envelope according to E t t τ Q ( ζe )t e( t) e Q (@ E ) E e τ e page 5

6 river concepts ower and Q requirement If we consider the quality factor, it depends how the load / antenna is matched to the source / driver: ow output impedance Q NT ~ Q Y, e.g. ~ 1.5 Y ~ NT ~ 1/Q NT, e.g. ~ 400 mw OUE ~ 0 NTENN 50 Ω oad Matching Q NT ~ Q Y, e.g. ~ 5 Y ~ OUE NT ~ NT ~ /Q NT e.g. ~ * 00 mw OUE 50 Ω NTENN 50 Ω We need a certain operational system Q to achieve time constants for modulation (e.g. ~ 1.5). In oad Matching, Q Y is half the value of the open antenna Q NT can be doubled. The power consumed in the antenna is related to 1/Q. For oad Matching, the required total power is the same, as for low output impedance. But for low output impedance no power is dissipated in the amplifier, all in the antenna network. page 6

7 ower and Q requirement The unloaded H-field strength emitted by an antenna with resonance at carrier frequency can be approximated by... U I I Z Q H X ~ I jx I NT Q U where Q Q X NT NT N river ower in Watt to 50 Ohm load 0,5 0,5 0,4 0,4 0,3 0,3 0, 0, 0,1 ower onsumption over H -field strength Q 35 Q 30 Q 5 Q 0 Q 15 1,4 1,5 1,6 1,7 1,8 1,9,0,1 H -field strength in /m (rms) page 7

8 Modulation envelope and Q requirement To emit high H-field from low driver power, Q should be high, To meet modulation timing specifications, Q should be low Q is only clearly defined for a single-resonance circuit. For this we get for IO/E14443 Type B specifications a maximum system Q tart of t f End of t f End of tr tart of t r hr tf tr h f 1 b 0 t To note: Modulation index and overshoots may be even more stringent! page 8

9 Modulation envelope and Q requirement For Type specifications % 100 % 90 % tart of t 1 60 % End of t 3 tart of t End of t % End of t 1and t tart of t 3 and t 4 t t 4 t t1 t3 page 9

10 Network transformation: : single-ended ended,, differential In practice, the TX output is usually differential (to be able to have double output voltage swing from a single supply voltage). For simplicty reasons, F ystem behaviour can be considered for a singleended network. omponent values for the differential network can then be calculated by the following considerations: - ource and load (antenna) impedance is split up for single-ended consideration erial components: arallel components: V ½ ½ V ½ ½ ½ ½ V ½ ½ V ource Network oad ource Network oad ource Network oad ource Network oad IFF 1 INGE IFF 1 INGE IFF INGE IFF 1 INGE IFF 1 INGE IFF INGE page 10

11 Network transformation: : single-ended ended,, differential o for the typical matching network, values for a single-ended equivalent circuit are following quantities of the differential network: ½ ½ V ½ ½ V & ½ ½ V ½ ½ V ource Network oad ource Network oad ource Network oad ource Network oad Z IN Z NT 0 ½ 1 Q V ½ 0 ½ 0 0V GN NT k, M NT NT T T T V_ V_ V _ imiter & ectifier page 11

12 Impedance Matching: π or T topology ny complex load can be matched to a source impedance using an element network in π - or T topology (general solution). s the antenna impedance varies over frequency, this matching is for the carrier frequency only. Z 1 Z Z Z 3 Z Z B Z Z ( ϕ) j sin( ϕ) sin( ϕ) ( ) cos j cos 1 1 ϕ ( ϕ) j sin( ϕ) sin( ϕ) ( ) cos j cos 1 ϕ Z Z B ( ϕ) sin sin( ) j j cos( ) 1 ϕ cos( ) ϕ ϕ ( ϕ) sin sin( ) j j cos( ) 1 ϕ cos( ) ϕ ϕ 1 1 Z j 3 sin( ϕ) ϕ...hase deviation output to input Z j sin( ϕ ) iterature: F. E. Terman, Network Theory, Filters, and Equalizers page 1

13 Towards a more specific impedance adjustment ny complex load can be matched to any source impedance using π - or T topology. However, there is at least one inductor, which introduces losses We may not need to adjust any load: - antennas are an inductive load (1 st self-resonance > f ) - phase relation output to input for the carrierfrequency is irrelevant o there is a more specific solution, consisting only of capacitors - HF capacitors of 0G or N0 have negligible losses and less tolerance - ess components also means reduction of costs and B area page 13

Impedance adjustment with -topology ZE ZM Z IVE EM-FI MTHING NTENN f E >> f U 0 0 M E M Q >> > ( ) Q Y j Z 1 j n equivalent circuit of the loop antenna may have the above structure.

14 Impedance adjustment with -topology ZE ZM Z IVE EM-FI MTHING NTENN f E >> f U 0 0 M E M Q >> > ( ) Q Y j Z 1 j n equivalent circuit of the loop antenna may have the above structure. It can be extracted from measurement. omplex antenna impedance Z can be calculated (over angular frequency ) Ω j( π Hz H ) ( π Hz 0.58Ω F ) ( π Hz) 6 1 j [ H F] (@ MHz) j Z 1 Z page 14

15 ntenna coupling NF antenna only oupling affects antenna impedance significantly - mutual inductance changes - oading Q changes Impedance trace is shown in mith hart distance variation to loading antenna coupling factor k varies page 15

16 Q-factor adjustment for operating frequency The quality factor of the antenna conductor shall be high above the intended Q-factor for operation at the carrier frequency MHz. We can neglect losses in the capacitor (if good components are chosen) - For one frequency, the serial equivalent circuit can be calculated to an equivalent parallel circuit for the inductor, using the Q equation: Q EI E - This way, an external resistor in series to the antenna allows to adjust the intended Q : E - To note: This can again be recalculated to a new antenna E QINTENE impedance Z (which might also be a parallel equivalent circuit). page 16

17 Impedance adjustment with -topology ZE ZM Z IVE EM-FI MTHING NTENN fe f U 0 0 No EM M M E Im { Z} 0 e{ Z} EIE j Z 1 j Z M Z E 1 j Z ( M M ) ( j Z ) M M M M M ( ) M p ± [ ] ( ) 1 ( ) p 4 q p ( 1 ) 6 ( ) 4 M q 4 page 17

18 page 18 nnex: Exact derivation of reactance matching nnex: Exact derivation of reactance matching with capacitors (I): with capacitors (I): ( ) s s s s s Y U NTENN MTHING IVE ( ) T s s s s s Y Z ( ) [ ] ( ) Nenner s s s s s 3 ( ) ( ) [ ] s s s s s 3 - The admittance of the parallel equivalent antenna circuit and is given by - Impedance for the parallel equivalent circuit of antenna and reactance matching network is... - This impedance is set equal to the desired real ( reactance matching) source impedance (e.g. 50 Ω).

19 page 19 ( ) ( ) [ ] j j j 3 ( ) j j j 3 ( ) a, ( ) [ ] ( ) ( ) G b, - Transition s j and coefficient comparison of real and imaginary parts: - Imaginary parts: - eal parts: - Both solutions for are set equal, to solve for nnex: Exact derivation of reactance matching nnex: Exact derivation of reactance matching with capacitors (II): with capacitors (II):

20 page 0 ( ) ( ) ( ) 4 [ ] [ ] ( ) [ ] p ( ) ( ) G q q p p b a ± 4, - For, a, b follows... - ort according the power of : - esolve the characteristic equation, cancel: - Knowing allows to calculate using one or the other equation. Note: only positive, real values have a physical meaning! nnex: Exact derivation of reactance matching nnex: Exact derivation of reactance matching with capacitors (II): with capacitors (II):

21 ntenna coupling no EM filter TX 1 V ½ 1 ½ Q NT k, M NT 0 0V GN NT distance 80 3 mm page 1

22 easoning for extending the network ue to tandard (e.g. IO/IE14443) requirements for modulation timing, the allowable Q-factor for the operated system is rather low (~limited bandwidth). For efficient H-field emission, a higher reactive current is desirable a nd resonance frequency can increase the bandwith. Furthermore, this nd resonance ( low-pass) can suppress unwanted harmonics emission ( name EM filter) This comes on the expense of more signal distortions page

23 Impedance adjustment with -topology ZE ZM Z IVE EM-FI MTHING NTENN f E f U 0 0 M M E Im { Z} 0 e{ Z} EIE j Z 1 j Z M 1 j Z ( M M ) ( j Z ) M M M Z E Z M j Z 0 M j page 3

24 Impedance adjustment with -topology For the calculation of and we follow a more systematic approach and recalculate a real and imaginary impedance for every step: 1 st step: starting from right side, we calculate an antenna impedance Z e X ( X X ) ( Z ) a Im X X X X ( X X ) ( Z ) Xa page 4

25 Impedance adjustment with -topology nd step: starting from the left side, we calculate the EM filter impedance and the adjustment network impedance Z M 1 X 0 0 X 0 0 e 0 X 0 M 0 ( X 0 X 0 ) ( Z ) m Im X 0 X 0X 0 0 M jx 0 ( Z ) 0 ( X X ) 0 0 Xm page 5

26 page 6 This way, we bring the matching condition in the middle of the network. 3 rd step: olving condition for the parallel and serial capacitance (target impedance): ± 1 1, a m a m a a a m a m X X X ( ) a a a a a m X X X X X X X X X 1 X 1 Finally, we need to sort out solutions which have no physical meaning - only positive capacitance values have a representation - not all antennas can be matched (if we violate a pre-condition, it is not possible Note: In practice, the impedance must be checked by measurement, as parasitics may cause deviations from the ideal conditions Impedance Impedance adjustment with adjustment with -topology topology

27 ntenna coupling with EM filter 0 ½ 1 Q TX 1 V ½ 0 ½ 0 0V GN NT k, M NT NT distance 80 3 mm page 7

28 Which loads can be matched? For the capacitor network, the area in the mith hart is following eference: Electronic pplications of the mith hart by hillip H. mith, 1969, p. 14 FOBIEN E page 8

29 Which loads can be matched? For the network with EM-filter, it is slightly more difficult We need to calculate a target impedance (Z T ) first, which depends on our desired input impedance Z IN, and the (loaded) antenna impedance (Z ). Ztarget (Z T ) Z T ZIN jx 0 1 jx0( jx 0 Z IN ) Z IN 0 Z NT 1 Q k, M V V V TX 1 0V GN TX NT B I_NT NT NT T T T V_ 0 1 Q B V _ ifferential EM-Filter lumped component impedance adjustment network antenna equivalent circuit I antenna equivalent circuit I equivalent circuit page 9

30 Which loads can be matched? ntenna impedance Z (including coupling) egion, which can be matched to desired network input impedance djustable range for parallel cap - - djustable range for serial cap Target impedance Z T Network input impedance Z IN (@ carrier frequency) Frequency trace of Z IN page 30

31 Which loads can be matched? The region of network input impedances Z IN at carrier frequency, which can be adjusted to an intended resistance ( matched ), is limited by two circles. For the parallel capacitor, from short to Z T For the serial capacitor, from Z T to open. The limit circle is given by - x T, y T. coordinates of Z T c - c center, r radius ( 1 x y ) T ( x 1) T T r 1 c The limit circle is given by c ( 1 x y ) T ( x 1) T T r 1 c Impedance adjustment possible, iff e Im ( Z ) e( Z T ) ( Z ) 0 ( inductive load ) page 31

32 The resonant coupling system eader equivalent circuit properties,, NF hip analogue front end V MI XB TXB GN TX X EM-Fil. 0 0 eceive path Matching network Q ntenna Transponder equivalent circuit properties,, ntenna ssemb. hip roximity hip V MI coupling k esonant system properties k, f, Q E tandard defines properties at the ir Interface page 3

33 How near-field coupling affects the air interface oupling: 0 % istance: -- mm Matching-Impedance 0 0 EM-FI s p MTHING NTENN 110 % 100 % 90 % tart of t 1 60 % End of t 3 tart of t End of t % End of t 1 and t tart of t 3 and t 4 t t 4 t t 1 t3 page 33

34 How near-field coupling affects the air interface oupling: 6 % istance: 5 mm Matching-Impedance 0 0 EM-FI s p MTHING NTENN t1 in τ t in τ t3 in τ t4 in τ a H OV page 34

35 How near-field coupling affects the air interface oupling: 13 % istance: 15 mm Matching-Impedance 0 0 EM-FI s p MTHING NTENN t1 in τ t in τ t3 in τ t4 in τ a H OV page 35

36 How near-field coupling affects the air interface oupling: 1 % istance: 10 mm Matching-Impedance 0 0 EM-FI s p MTHING NTENN t1 in τ t in τ t3 in τ t4 in τ a H OV page 36

37 How near-field coupling affects the air interface oupling: 38 % istance: 5 mm Matching-Impedance 0 0 EM-FI s p MTHING NTENN t1 in τ t in τ t3 in τ t4 in τ a H OV page 37

38 Thank you for your udience! lease feel free to ask questions... page 38

RLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is

RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge