RF and Microwave Transformer Fundamentals by Mini-Circuits

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 ety of types; our focus is on Primary Secondary 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 Figure 4. Figure 3:Fig Transformer 2 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 neglecting the small insertion flux is dependent on the applied + I1 I2 + 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 number 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 to voltage and current direction realized. Fig 4

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 Balun 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 Dual anced impedance to unbal- Ampli er system performance such as anced and vice versa. signal-to-noise ratio. Port #1 Port #3 +V D0 In addition, Baluns can 2V D0 In case (ii), the interfering 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 device. When the output of VDI -V D0 example of the same is shown - 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- Figure 7: Dual amplifierFig 7excited by differential Signals 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- Port #1 Port #3 +V C0 let us use as an example a 0V 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 VCI amplifiers are identical and the +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- Figure 8: Dual amplifierFig excited 8 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

Dual a single-ended output. IP2 of Ampli er +V C0 Wideband communication such an amplifier is in excess Port #1 Port #3 +V D0 systems have signals occupy- 2V D0 of 87 dBm. ing multi-octave frequency Figure 12 shows a push- R S1 T1 range. For example, CATV pull amplifier using transistors. + signals occupy 50-1000 MHz Port #2 Port #4 Base biasing is applied through VDI range, which is more than four +V C0 center tap of T1 and collectors octaves. Such signals when - R S2 through T2. Configurations + -V D0 amplified in conventional - A,B and F can be used for this VCI amplifiers can be distorted due 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 signal 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 balanced signal is applied to the See Table 1 for the sche- T1 T2 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- RF-Out 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 Fig 12 in HELA-10, and combined in 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 (V2/V3)

Phase unbalance (in degrees) = θ (in degrees)

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 connected 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 impedance 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 cuits.com/pages/pdfs/howxf- 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

Applications Conversion Impedance Balun Balanced Balanced to Frequency Impedance Power (MHz) ratio DC handling Schematic Description Typical Typical Unbalance Isolation Typical maximum maximum use range ratio Configuration DC isolated primary and 0.01 to secondary, center-tap 1 to 16 Excellent Yes Up to 1W YES YES YES A 1400 secondary DC isolated primary and 0.004 to Up to 0.25 secondary, center-tap 1 to 25 Excellent Yes YES YES YES B 500 W primary and secondary DC isolated primary and 0.01 to Up to 0.25 1 to 36 Average Yes YES YES YES C secondary 1200 W 0.05 to Up to 0.25 Auto transformer 0.1 to 14 N/A No YES -- -- D 2200 W DC isolated, three Up to 0.25 open windings, Tri-filar 0.01 to 200 1 to 2 Good No YES YES YES F W transformer Transmission line Up to 0.5 to 3000 1 to 4 Good No YES YES YES G transformer 2 W Transmission line Up to transformer-four 10 to 4500 2 & 4 Good No YES YES YES H 5 W windings 600 to Marchand Balun 1 to 4 Excellent Yes 3 W YES YES -- J 6200 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 cuits.com/cgi-bin/ modelsearch?model=hela-10, 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:// minicircuits.com/products/ transformers.html

Figure 19: Unbalance- Polar representation