RF and Microwave Transformer Fundamentals

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					PAGE 1 • OCTOBER 2009                        FEATURE ARTICLE                                                   www.mPdiGEsT.COm

RF and Microwave Transformer Fundamentals
by Mini-Circuits

Introduction                                                                                            another (secondary). At high
The purpose of this application                                                                         frequencies, the inter-winding
note is to describe the funda-                                                                          capacitance and magnet wire
mentals of RF and microwave                                                                             inductance form a transmission
transformers and to provide                                                                             line which helps propagate the
guidelines to users in selecting                                                                        electromagnetic wave from pri-
proper transformer to suit their                                                                        mary to secondary. The com-
applications. It is limited to                                                                          bination of magnetic coupling
core-and-wire and LTCC trans-                                                                           and transmission line propaga-
formers.                                                                                                tion helps the transformer to
                                                                                                        achieve outstanding operating
What is a Transformer?                                                                                  bandwidths (1:10000 or more).
A Transformer is a passive device                                                                       Figure 3 shows ideal circuit of
that “transforms” or converts a                                                                         a simplified two-winding trans-
given impedance, voltage or cur-                                                                        former.
rent to another desired value.        Figure 1: Open Case Transformer (Binocular Core)
In addition, it can also provide                                                                        Dot Convention of Ideal
DC isolation, common mode                                                                               Transformer
rejection, and conversion of bal-                                                                       If at the dotted end of the pri-
anced impedance to unbalanced                                                                           mary winding the voltage is
or vice versa, as explained later.                                                                      positive with respect to the un-
Transformers come in a vari-                                                                            dotted end, then the voltage at
                                                                       Primary             Secondary
ety of types; our focus is on                                                                           the dotted end of the secondary
transformers used in RF and                                                                             is also positive with respect to
Microwave signal applications.                                                                          the un-dotted end as shown in
Essentially, an RF transformer                                                 Fig 2                    Figure 4.
                                                                       Figure 3: Transformer
consists of two or more wind-                                                                              Also, if primary current flows
                                                                       Equivalent Circuit
ings linked by a mutual mag-                                                                            into dotted end of the primary
                                      Figure 2: Toroidal Core
netic field. When one winding,                                                                          winding, current flows out of
the primary has an ac voltage                                                                           the dotted end of secondary
applied to it, a varying flux is                                                                        winding (at low frequencies,
developed; the amplitude of the
flux is dependent on the applied         +      I1                                 I2      +
                                                                                                        neglecting the small insertion
                                                                                                        phase, current I1 entering the
current and number of turns                                                                             dot at primary is in phase with
in the winding. Mutual flux                                                                             current I2 exiting the dot).
linked to the secondary winding                                                                            In Figure 4, N1 and N2 are
induces a voltage whose ampli-                                                                          number of turns and V1 and
tude depends on the number of           V1              N1                   N2            V2           V2 are voltages at the primary
turns in the secondary winding.                                                                         and secondary respectively.
By designer’s choice of the num-
ber of turns in the primary and                                                                         Transformer Equations
secondary windings, a desired            -                                                 -
step-up or step-down voltage/
                                      Figure 4: Transformer showing dot convention with respect
current/impedance ratio can be
realized.                                                 Fig 4
                                      to voltage and current direction

Why are Transformers                      circuits; example: push-    the core can be binocular as
Needed?                                   pull amplifiers, ICs with   in Figure 1, toroid (doughnut
Transformers are used for1:               balanced input such as A    shaped) as in Figure 2 etc.
  •	 Impedance matching to                to D converters.            Wires are welded or soldered to
      achieve maximum power            •	 Common mode rejection       the metal termination pads or
      transfer between two                in balanced architectures   pins on the base. The core and
      devices.                                                        wire ensemble is housed in a      Faraday’s law of induction
  •	 Voltage/current step-up         How are they made?               plastic, ceramic or metal case.   states that, the voltage V
      or step-down.                  An RF transformer usually                                          induced in a coil is equal to the
  •	 DC isolation between            contains two or more insulated   Ideal transformer                 change of magnetic flux link-
      circuits while affording       copper wires twisted together    At low frequencies, an alter-     ages NΦ with respect to time.
      efficient AC transmis-         and wound around or inside       nating current applied to one     Based on the above, transform-
      sion.                          a core, magnetic or non-mag-     winding (primary) creates a       er equations shown above are
  •	 Interfacing between bal-        netic. Depending on design       time-varying magnetic flux,       derived2.
      anced and unbalanced           and performance requirements,    which induces a voltage in           It states that the output volt-
PAGE 2 • OCTOBER 2009                            FEATURE ARTICLE                                                                  www.mPdiGEsT.COm

age (V2) is equal to turns ratio                                                                                           a wonderful job in rejecting the
(n) times the input voltage                                                                                                common mode signal and com-
(V1). It also states that, output                                                                                          bining the differential mode
current (I2) is input current (I1)                                                                                         signals.
divided by the turns ratio and       Balanced                                                            Unbalanced           To illustrate the benefits of
output impedance (Z2) is input       Impedance                                                           Impedance         common mode rejection in a
impedance (Z1) multiplied by                                                                                               Balun, let us take two exam-
the square of the turns ratio.                                                                                             ples:
For example;                                                                                                                  i. a PC board having sin-
if n=2 and Z1=50 ohms:                                                                                                             gle ended devices (such
V2=2V1                                                                                                                             as amplifiers, mixers
I2=I1/2 and                           Figure 5: Balun                              Fig 5                                           etc.) interconnected with
Z2=4Z1 = 200 ohms                                                                                                                  unshielded transmission
                                                                                                                                   lines such as microstrip
What is a Balun?                                                                                                                   and
Before defining what a Balun                                                                                                  ii. a PC board having bal-
is, we need to define balanced       Balanced                                                            Unbalanced                anced devices intercon-
and unbalanced impedances.           Impedance                                                           Impedance                 nected with unshielded
   A balanced two-terminal                                                                                                         transmission lines.
impedance has neither of its                                                                                                  In case (i) any in-band inter-
terminals connected to ground,                                                                                             fering signal, such as radiation
whereas an unbalanced imped-                                                                                               from adjacent circuits, is added
ance has one its terminals con-                                                                                            to the desired signal and there
nected to ground; see Figure          Figure 6: Transformer can function as a Balun                                        is no way of separating the
5. By definition, a balun is a                                                      Fig 6                                  wanted from the unwanted.
device which transforms bal-                                                                                               This results in degradation of
anced impedance to unbal-                                              Ampli er                                            system performance such as
anced and vice versa.                                                                                                      signal-to-noise ratio.
   In addition, Baluns can
                                                            Port #1                Port #3    +V D0                           In case (ii), the interfering
                                                                                                                2V D0
provide impedance transfor-                                                                                                signal is of equal amplitude
mation, thus the name Balun          R S1                                                           T1                     (due to close proximity) on
Transformer. Most transform-             +                  Port #2                Port #4                                 both lines feeding a balanced
ers can be used as baluns, an               VDI                                                                            device. When the output of
example of the same is shown
                                                                                              -V   D0
                                                                                                                           such balanced device is con-
in Figure 6.
                                         -                    R S2                                                         verted into single ended by
                                                                                                                           using a balun, the interfering
Applications of Transformers/                       VDI                                                                    signal, which is common mode
Baluns-Examples                                     +                                                                      in nature, is rejected.
Common mode rejection                                                                                                         In an ideal balun, signals
One of the most common appli-
                                                           Fig excited by differential Signals
                                      Figure 7: Dual amplifier 7                                                           appearing at the output of
cations of a balun is for com-                                                                                             balanced ports are of equal
mon-mode signal rejection.                                                                                                 amplitude and differ in phase
   To illustrate common mode                                            Dual                                               by 180º. In reality, even in
                                                                        Ampli er
rejection properties of a balun,                                                                                           a well designed balun/trans-
let us use as an example a                                   Port #1                Port #3    +V C0                       former, there is a small ampli-
dual amplifier in cascade with                                                                                             tude and phase unbalance.
a 1:1 transformer (balun). It is       R S1                                                             T1                 Amplitude unbalance is differ-
assumed in this example that                 +               Port #2                Port #4                                ence in amplitude (in dB) and
the s-parameters of the dual                                                                                               phase unbalance is deviation
amplifiers are identical and the
                                              VCI                                              +V C0                       from 180º phase, in degrees.
balun is ideal.
                                             -                 R S2                                                        A well designed transformer
   When two signals VDI of                              +                                                                  might have 0.1 dB amplitude
equal magnitude but opposite                            VCI                                                                and 1º phase unbalance in the
polarity (differential signals),                        -                                                                  mid-band. Unbalance results in
are applied to the inputs of a                                                                                             common mode rejection being
dual amplifier, they are ampli-                              Fig 8
                                      Figure 8: Dual amplifier excited by common mode signals                              finite instead of nearly infinite.
fied and appear at the output
as two signals of equal magni-       polarity (common mode sig-                         T1 (balun), where they cancel      Push-Pull amplifiers3
tude (VDO) but opposite polar-       nals) are applied to the inputs                    and result in a signal of magni-   Benefits:
ity as shown in Figure 7. These      of a dual amplifier, they are                      tude 0V at output of T1.             •	 Even-order harmonic
signals are combined in T1 (1:1      amplified and appear at the                           In real life both unwanted            suppression, which is
Balun) and result in a signal of     output as two signals of equal                     common mode and wanted dif-              a big deal in wideband
magnitude 2VDO.                      magnitude (VCO) and of same                        ferential signals are applied to         Cable TV application
   When two signals VCI of           polarity as shown in Figure 8.                     the input of dual amplifier as       •	 ~3 dB higher Pout & IP3
equal magnitude and same             These signals are combined in                      shown in Figure 9. Balun does            than a single device.
PAGE 3 • OCTOBER 2008                        FEATURE ARTICLE                                                     www.mPdiGEsT.COm

                                                                 Ampli er              +V C0              a single-ended output. IP2 of
   Wideband communication                             Port #1                Port #3   +V D0              such an amplifier is in excess
systems have signals occupy-                                                                      2V D0   of 87 dBm.
ing multi-octave frequency                                                                                   Figure 12 shows a push-
range. For example, CATV
                                     R S1                                                  T1
                                                                                                          pull amplifier using transistors.
                                         +            Port #2                Port #4
signals occupy 50-1000 MHz                                                                                Base biasing is applied through
range, which is more than four              VDI                                        +V C0              center tap of T1 and collectors
octaves. Such signals when               -
                                                        R S2                           -V D0              through T2. Configurations
amplified in conventional                         -                                                       A,B and F can be used for this
amplifiers can be distorted due             VCI   VDI                                                     application. By using blocking
to the second order products                      +                                                       caps, at input, configuration H
generated inside the amplifier.                        +                                                  can be used.
For example, second harmonic                      VCI
of 50 MHz signal is 100 MHz,                            -                                                 Power Splitter 180º
so also second harmonic of 400                                       Fig 9                                Output signals of an ideal
MHz which is 800 MHz and                                                                                  transformer are of equal mag-
both are within the band. An          Figure 9: Dual amplifier excited by common mode and                 nitude and of opposite phase as
ideal push-pull amplifier can         differential signals                                                shown in Figure 13 and hence
cancel the internally generated                                                                           can be used as a 180° splitter.
products and preserve the sig-
nal quality. Figure 10 shows a                                                                            Double Balanced Mixer
simplified schematic of such an                                                                           In its simplest form, it con-
amplifier. It consists of two bal-                                                                        sists of a pair of 1:4 baluns/
uns and two identical amplifi-                                                                            transformers and a diode quad.
ers. When a signal is applied                                                                             Center tap of the LO trans-
to the input of the first balun                                                                           former is grounded and center
(Balun #1), the output signal                                                                             tap of the RF Balun (right)
from the same balun consists of                                                                           is used for extracting IF (See
two signals of equal amplitude                                                                            Figure 14).
and out of phase. These signals
are amplified combined in out-                                                                            Converting single ended to
put balun (Balun #2).                                                                                     balanced
   The gain of a push-pull                                                                                Many ICs available in the mar-
amplifier is same as that of          Figure 10: Simplified Schematic of Push-Pull Amplifier              ket have balanced input/output
an individual amplifier, where-                                                                           terminals. When such ICs have
as the output power is twice                                                                              to be interfaced with unbal-
that of an individual ampli-                                                                              anced circuits, transformers/
fier. Push-pull connection is                                                                             baluns are used. Example of
frequently used for combining                                                                             the same is shown in Figure
power of individual amplifiers.                                                                           155.
   An additional benefit, push-
pull amplifiers cancel even-                                                                              Transformer Configurations6
order harmonics, as even-order                                                                            Transformer configurations can
harmonics are in-phase. An                                                                                be broadly classified as:
example is shown in Figure 11                                                                               1. Conventional;
for second harmonic. Same is                                                                                    core-and-wire
true for other even order prod-                                                                                 based(Configurations
ucts falling within the operating                                                                               A,B,C,D,F)
bandwidth of the transformer.         Figure 11: Even-order harmonics cancelled in push-pull                2. Transmission line; core-
   As an example, Mini-Circuits       amplifier                                                                 and-wire and LTCC
HELA-10+ consists of a pair of                                                                                  (Configuration G,H,K)
amplifiers4. As they are on the                                                                             3. Marchand; LTCC
same chip, their gain and phase              V+                                                                 (Configuration J)
are very well matched. If a bal-
anced signal is applied to the                              T1                                               See Table 1 for the sche-
input of the HELA-10+ then           RF-In                                                                matics, frequency of operation,
the output is also balanced.                                                                              impedance ratio, important
By using a set of baluns (or                                                                              electrical parameters and appli-
transformers) at the input and                                                                            cations.
output a single ended input                                                                                  Conventional transformers
is first converted into a bal-                                                                            made of core-and-wire option-
anced signal in T1, amplified                                                                             ally have center tap on primary
in HELA-10, and combined in                                         Fig 12
                                      Figure 12: Push-Pull amplifiers using Transistors & Baluns          or secondary or on both sides
the transformer T2 to produce                                                                             and are limited to an upper
PAGE 4 • OCTOBER 2008                       FEATURE ARTICLE                                                          www.mPdiGEsT.COm

                                                                                                 defined as:

                                                                                                 Amplitude unbalance in (dB) = 20 log10

                                                                                                 Phase unbalance (in degrees) = θ (in

                                                                                                 Test Characterization of Transformers
                                                                                                 Insertion Loss
  Figure 13: 180° Splitter             Figure 14: Double balanced mixer                          Prior to the availability of modern network
                                                                                                 analyzers, baluns and transformers having
                                                                                                 impedance ratio other than 1:1 were con-
                                                                                                 nected back to back and the combined
                                                                                                 insertion loss of two units was measured.
                                                                                                 Insertion loss of a single device was calcu-
                                                                                                 lated by dividing the measured loss by 2.
                                                                                                 This overcame the need to match imped-
                                                                                                 ance of devices having output impedance
                                                                                                 other than 50 ohms.
                                                                                                    In recent years, baluns have been char-
                                                                                                 acterized as 3-port networks, like a two-
                                                                                                 way 180° splitter. As the impedance at
                                                                                                 the secondary ports is generally not 50
                                                                                                 ohms, impedance transformation is essen-
                                                                                                 tial to do an accurate measurement. One
                                                                                                 method is to use resistive matching pads
  Figure 15: Baluns used at input & output to convert from and to single ended                   at the secondary1 for that purpose. In
                                                                                                 this method insertion losses from primary
                                                                                                 dot to secondary dot and primary dot to
frequency of 2 GHz. Most configurations             iv. For DC isolation between primary         secondary are measured. The average of
have DC isolation from primary to second-               and secondary, do not choose trans-      these two losses after subtracting the loss
ary.                                                    mission line configurations (G, H,       of the matching pad and 3 dB for loss due
   Transmission line type transformers                  K,). If needed; add DC blocking          to theoretical split, is specified as insertion
using core-and-wire operate to 3 GHz and                caps to isolate primary and second-      loss.
using LTCC to 5 GHz or higher and do                    ary.                                        New network analyzers such as Agilent’s
not have DC isolation from primary to                                                            PNA series provide impedance transforma-
secondary. External blocking capacitors           Characteristics of Transformers                tion and port extension capabilities so that
are needed to realize isolation.                  Insertion Loss                                 there is no need to add resistive matching
   Marchand (named after the inventor)            Figure 16 shows the insertion loss of a        pads. A PNA analyzer enables 3-port mea-
transformers operate to 6 GHz and higher          core-and-wire transformer. The low-end         surement for any user-defined input and
and are realized in LTCC form and have            loss is heavily influenced by the prima-       output impedances.
DC isolation from primary to secondary.           ry inductance while the high-end loss is
   Selection of a transformer for an appli-       attributed to the losses in inter-winding      Unbalance: Amplitude and Phase
cation can often be confusing and some-           capacitance, and series inductance.            The set up used for charactering a trans-
times results in the wrong choice. The               The permeability of a magnetic core is      former as a 3-port network provides two
following guidelines attempt to clarify the       influenced by temperature. As the tem-         insertion losses (primary dot to second-
options and state the benefits of various         perature decreases, permeability decreases     ary dot and primary dot to secondary)
configurations.                                   causing an increase in the insertion loss at   in vector form. The difference of these
   i. For impedance matching (unbal-              low frequency.                                 two magnitudes in dB is called amplitude
        anced to unbalanced) applica-                Figure 17 shows the insertion loss of an    unbalance. The phase angle deviation from
        tions; choose auto transformer            LTCC transformer. Note the insertion loss      180° is phase unbalance.
        (Configuration –D), in general it         is low over the entire band as the losses in
        provides lowest insertion loss.           ceramic are minimal and variation with         Input Return Loss
   ii. For Balun applications, choose a           temperature is also minimal.                   When the secondary is terminated in its
        balun with center tap on balanced                                                        ideal impedance, the return loss measured
        side as it provides excellent amplitude   Unbalance: Amplitude and Phase                 at the primary is the input return loss. It is
        and phase balance (Configurations         An incident voltage (V1) is transformed        a measure of the effectiveness of the balun
        A, B, H, J).                              into two voltages V2 and V3 (see Figure        in transforming impedance.
   iii. For Balanced to balanced transfor-        18). In an ideal transformer, the amplitude
        mation, choose a transformer with         of V2 is equal to that of V3 and the phase     S-Parameters
        center tap on both primary and            difference is 180º. In practical transform-    By using a multi port network analyzer,
        secondary (Configuration B, L) as         ers there is small amplitude difference and    s-parameters can be measured. The result-
        it provides excellent amplitude and       the phase difference deviates from 180º        ing “.snp” file is in Touchstone format and
        phase balance on both sides.              (see Figure 19). Amplitude unbalance is        can be used in simulators such as Agilent
PAGE 5 • OCTOBER 2008                        FEATURE ARTICLE                                                                www.mPdiGEsT.COm

    Figure 16: Insertion Loss vs. frequency of core-and-wire                     Figure 17: Insertion Loss vs. frequency of an LTCC
    transformer                                                                  transformer

ADS.                               Summary                                                                       Circuits”, McGraw-Hill Book
   When an application needs       This application note is to              References                           Company, Second edition,
impedance other than the one       describe the fundamentals of               1) Mini-Circuits Application       1983
specified in the data sheet,       RF and microwave transform-              Note, “How RF Transformers              3) R.Setty, “Push-pull ampli-
“.snp” can be used in simula-      ers, most common applications,           Work”, http://www.minicir-           fiers improve second-order
tion software such as Agilent’s    guidelines to users in selecting          intercept point”, RF Design,
ADS (or equivalent ) to analyze    proper transformer to suit their         merwork.pdf                          P76, Nov 2005
its performance.                   applications and measurement               2) Nathan R. Grossner,                4)Mini-Circuits         web-
                                   methods.                                 “Transformer for Electronic          site,     http://www.minicir-

     Table I: Summary of Transformer Configurations




                                                                                                                                                      Balanced to
                                                          Frequency     Impedance

                                                           (MHz)        ratio
                                                                                                   DC          handling
                 Schematic     Description                Typical       Typical       Unbalance
                                                                                                   Isolation   Typical
                                                          maximum       maximum
                                                          range         ratio
                               DC isolated primary and
                                                          0.01 to
     A                         secondary, center-tap
                                                                        1 to 16       Excellent    Yes         Up to 1W       YES            YES         YES
                               DC isolated primary and
                                                          0.004 to                                             Up to 0.25
     B                         secondary, center-tap
                                                                        1 to 25       Excellent    Yes
                                                                                                                              YES            YES         YES
                               primary and secondary
                               DC isolated primary and    0.01 to                                              Up to 0.25
     C                         secondary                  1200
                                                                        1 to 36       Average      Yes
                                                                                                                              YES            YES         YES

                                                          0.05 to                                              Up to 0.25
     D                         Auto transformer
                                                                        0.1 to 14     N/A          No
                                                                                                                              YES              --         --
                               DC isolated, three
                                                                                                               Up to 0.25
     F                         open windings, Tri-filar   0.01 to 200   1 to 2        Good         No
                                                                                                                              YES            YES         YES
                               Transmission line                                                               Up to
    G                          transformer
                                                          0.5 to 3000   1 to 4        Good         No
                                                                                                                              YES            YES         YES
                               Transmission line
                                                                                                               Up to
     H                         transformer-four           10 to 4500    2&4           Good         No
                                                                                                                              YES            YES         YES
                                                          600 to
      J                        Marchand Balun
                                                                        1 to 4        Excellent    Yes         3W             YES            YES          --

     K                         Transmission line          5 to 3000     1             Excellent    No          Up to             --          YES         YES
                               transformer: Tri-Filar                                                          0.5W

      L                        Balnced to balanced        10 to 2200    1.5 to 2      Good         No          Up to          YES              --        YES
                               transformer                                                                     0.25W
PAGE 6 • OCTOBER 2008                 FEATURE ARTICLE       www.mPdiGEsT.COm
click link ”Data Sheet”
   5) Dorin Seremeta, “Accurate
Measurement of LT5514
Third Order Intermodulation
Products”, Linear AP note         Figure 18: Unbalance in
97-3                              Transformer
   6) “Transformers RF/IF”,
Mini-Circuits web page http://

                                  Figure 19: Unbalance-
                                  Polar representation

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Description: Introduction The purpose of this application note is to describe the funda- mentals of RF and microwave transformers and to provide guidelines to users in selecting proper transformer to suit their applications. It is limited to core-and-wire and LTCC trans- formers.