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 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 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- Amplier 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 Amplier 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 Amplier +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.