Passive Baluns in Modern Data Conversion Systems

Modern data conversion components utilize differential interfaces to enhance dynamic range, increase noise immunity, reduce harmonic distortion, and support high sampling rates. Differential signaling requires designers to convert single-ended signal sources to differential analog-to-digital converter (ADC) inputs and convert differential digital-to-analog converter (DAC) outputs to single-ended loads. Mini-Circuits’ passive balanced-to-unbalanced transformers (baluns) have become an essential component in many of these applications. Depending on the band plan of the radio and the speed of the ADC or DAC, these baluns can be found in the RF or IF section. Applications include SIGINT/ELINT, communications systems, test instrumentation, software-defined radio (SDR) systems and radars.

Since Mini-Circuits has published several articles on passive baluns and transformers that are referenced in this article^1,2,3,4, we only briefly touch on the fundamental principles of passive baluns. The central focus is to understand how baluns are applied to RF lineups that include ADCs and DACs, as well as some of the critical design tradeoffs and practical considerations. A generalized block diagram as well as references to examples from Texas Instruments’ lineup of ADCs and DACs are included. Read on to learn how simple passive baluns can solve sophisticated problems in the complex differential signaling space.

Side with Heaviside

British self-taught mathematician, physicist and electrical engineer Oliver Heaviside first described the theoretical mechanics of signal transmission lines beginning in 1876 when he formulated what is known as The Telegrapher’s Equations, detailing how voltages and currents propagate as waves along circuits (i.e. transmission line theory)⁵. Along with his invention of coaxial cable in England and revamping of Maxwell’s Equations, Heaviside provided the exact mathematical tools needed to model how waves travel through coax and balanced wire lines. Appendix A is dedicated to showing how Heaviside’s strong contributions laid the theoretical foundation for high-frequency circuit design, and the development of the ferrite core-based, wire wound and coaxial RF baluns.

The Big Difference in Data Conversion

The migration towards differential signaling architectures has been one of the most significant developments in high-speed and low bit error rate (BER) data conversion of recent decades. The vast majority of today’s ADCs and DACs for communications, test instrumentation, SDRs, EW systems and radar utilize differential analog interfaces.

Differential inputs (ADCs) and outputs (DACs) provide the following strategic advantages:

• Increased signal voltage swing
• Improved common mode rejection ratio (CMRR), or simply common mode rejection
• Reduced even-order harmonic distortion
• Decreased susceptibility to ground noise
• Improved electromagnetic compatibility (EMC) in terms of emissions as well as susceptibility
• Increased dynamic range

Despite their advantages, differential data conversion ADCs and DACs must interface with many practical subsystems that are already in place or being designed that are still single-ended. Many antennas and most all mixers, filters, amplifiers, and measurement equipment use 50Ω single-ended interfaces. Passive baluns provide a simple, broadband, low-noise solution for translating between these domains.

Passive Balun Basics

As mentioned previously, Mini-Circuits’ repertoire already includes several articles on baluns and transformers^1,2,3,4, so we only touch briefly on balun basics in this section. “Balun” is shorthand for “balanced-to-unbalanced” and refers to a conversion between styles of signal transmission. Most often, a single-ended signal (for which ground is the return path) is being converted into a differential pair, or vice versa. Additionally, as this conversion is performed, it is often convenient to convert from one impedance level to another. There are many different configurations and styles of baluns and transformers, and several different technologies that are used in their construction.⁶ Mini-Circuits’ recent article entitled “Lexicon of Balun and Transformer Configurations” describes many of these configurations. In a practical sense, we will focus on ferrite-based core and wire baluns and more specifically, 1:1 and 1:2 wideband RF balun transformers.

An ideal passive balun takes in a single-ended signal and without loss produces two output signals V₊ and V_– which are equal in amplitude and differ in phase by exactly 180⁰. In practical passive baluns, amplitude and phase unbalance exists, as well as some loss in signal amplitude in the conversion process, but no additional noise is introduced.

By contrast an active differential driver, such as a fully differential amplifier (FDA) will introduce amplitude and phase unbalance as well, but also requires a bias (power) supply and introduces noise into the system. An FDA can provide signal gain, however, not possible with a passive balun.

Many typical passive balun implementations can be found in [5] and include:

• Transmission-line transformers
• Autotransformers
• Ruthroff transformers
• Guanella baluns
• RF ferrite-core and wire balun transformers
• Planar LTCC microwave baluns
• Marchand baluns

The Benefits of Differential ADC Inputs for High-Speed ADCs

High-speed ADCs typically incorporate differential sample-and-hold structures, because differential inputs will always improve the signal-to-noise ratio (SNR) and spurious-free dynamic range (SFDR). Additionally, the balanced inputs inherently afford a reduction in even-order harmonic distortion and provide better common mode noise rejection, or CMMR, since it is invariably measured in dB as a ratio. Essentially, the ADC measures the difference between the two balanced inputs V₊ and V_– and rejects common mode signals impressed in phase upon both input signals simultaneously. High-speed ADCs are used in a multitude of RF systems such as surveillance systems, cellular base stations, radar systems, spectrum analyzers, electronic warfare receivers, software-defined radios, and defense radio communications.

Passive Baluns Driving Differential ADC Inputs

The first order of business when driving a differential ADC input with a passive balun is invariably to convert the single-ended 50Ω source into a balanced pair at the impedance level required by the ADC, most often 100Ω differential. There are plenty of other considerations with regard to signal level and frequency range, but first we convert by designing in our passive balun. Figure 1 shows a simplified block diagram of the passive balun performing the single-ended to differential conversion while effecting an impedance transformation of 50Ω to 100Ω simultaneously. The differential antialiasing filter is also shown between the balun and the ADC because it is commonplace in a great many RF systems.

Common Mode Noise Rejection and Even-Order Harmonic Distortion Suppression

A representative single-ended signal at the fundamental frequency is shown in the upper portion of the block diagram of Figure 1 along with the two differential balun outputs that are 180⁰ out of phase. Impedance transformation is shown, and isolation is inherent to the magnetic core. Excellent common mode rejection ratio (CMRR) and second order distortion reduction are inherent to this RF system which includes the balun. While the balun itself will merely pass through any common mode noise or second order distortion products already at its single-ended input, these signals manifest themselves as in-phase and common to both differential outputs. Since the differential ADC calculates the difference between its two input terminals, the difference between the two identical, in-phase signals (whether they’re common mode noise or second-order products) will ideally and theoretically be zero.

Any nonideal balun behavioral characteristics such as phase or amplitude imbalance will impact performance, but most often excellent cancellation is achieved.

Practical Example of a Passive Balun-Driven Texas Instruments’ High-Speed ADC Circuit

By examining the schematic and layout recommendations for a verified GSPS ADC design referenced by TI Designs High Speed,⁷ we find an RF core & wire Mini-Circuits’ 1:1 balun, the TC1-1-13MA+ driving the Q input. This balun operates from 4.5 to 3000 MHz and exhibits excellent amplitude and phase unbalance. The exact implementation can be found on Pages 1 through 3 of reference [7]. Finally, as an example of the type and speed of ADC that this balun is capable of driving, consider that the TI ADC12D1000RF variant is a 12-bit, dual 1.0-GSPS or single 2.0-GSPS, RF sampling ADC. Further information on passive matching baluns for use in high-speed ADCs can be found in [8] where the performance of Mini-Circuits’ TCM2-33WX+ 10 to 3000 MHz 1:2 core & wire balun is found to compare favorably to a significantly higher cost alternative.⁸

DACs and Their Use of Differential Outputs

The lower portion of Figure 1 shows a generalized block diagram for a DAC-based upconverter/transmitter. It is common for high-speed DACs to utilize differential outputs. The benefits of this differential architecture are similar to those described for the ADC. Improved signal linearity, lower harmonic distortion due to the cancellation of even-order harmonics, greater output power/signal amplitude and, specifically for the DAC, improved suppression of digital feedthrough all serve to enhance performance compared to their single-ended counterparts’ capabilities.

Using a passive balun either immediately after the DAC output stage or immediately following the reconstruction filter, as shown in Figure 1, results in a natural cancellation of common mode signals when the differential signals are combined through the balun. This capability is especially important in radio communications transmissions, SDRs, phased array radars, or in any RF system where the linearity of the transmitted signal is of paramount importance.

Practical Example of a Texas Instruments’ High-Speed DAC Driving a Passive Balun Circuit

To find a passive balun driven by a high-speed DAC we turn to the Evaluation Module User’s Guide for TI’s DAC39RF12EVM.⁹ In this user’s guide, two DAC outputs are set up for evaluation of different Nyquist zones, a low band for 3 to 6000 MHz differential output and a high band for the 1.8 to 18 GHz output. The configuration of the differential outputs and balun transformers can be found on pages 24 and 25 of the user’s guide for the low band and high band outputs, respectively.

The low band design on page 24 shows the differential DACOUTA outputs driving the TCM2-63WX+, a 30 to 6000 MHz 1:2 core & wire balun transformer. In order to effectively combine the differential DACOUTB outputs for the high band design, the Mini-Circuits’ MTX2-183+ 2 to 18 GHz 1:2 MMIC balun transformer was selected, as shown on page 25.

Balanced and Harmonious We’ve Made a Difference

Passive baluns are critical to modern data conversion systems. ADCs and DACs continue to gravitate towards differential architectures, so to achieve the superior dynamic range, linearity, and common-mode noise performance that is made possible by these architectures, baluns will continue to provide a viable means of interfacing with the single-ended world.

We discussed Heaviside and his contributions, ultimately relegating his foundational work to Appendix A. We then walked through the salient features of balun transformers and their ability to perform 180⁰ phase splitting, impedance transformation, common-mode and second order product rejection, and power combining without introducing active noise or consuming power.

A high-speed ADC design that utilizes a Mini-Circuits’ passive balun was examined and a high-speed DAC design with Mini-Circuits’ passive baluns referenced as well, both from Texas Instruments. These passive baluns served not merely as an interface component for data conversion, but as an enabling technology allowing these modern, high-speed data conversion products to achieve practical performance that approaches their full theoretical capability.

Appendix A – Oliver Heaviside and His Significant Contributions to RF Balun Design

Until the early 1800’s, conventional wisdom was that electric energy flowed like pushing a fluid through a pipe. That water-pipe analogy is often used as a teaching tool, with voltage analogous to water pressure, current to flow rate, and resistance to pipe constriction. Electricity and magnetism were thought to be completely separate entities,¹⁰ until 1820 when Danish physicist Hans Christian Oersted discovered that a magnetic effect was produced by an electric current flowing in a wire.¹¹ In classical electromagnetism, Ampère’s circuital law, often simply called Ampère’s law, and sometimes Oersted’s law, relates the circulation of a magnetic field around a closed loop to the electric current passing through that loop.¹¹

James Clerk Maxwell originally published the law in 1855, improved the law and in 1865 it became one of Maxwell’s equations that form the foundation of classical electromagnetism, and is often called the Ampère–Maxwell law.¹¹ Maxwell also published “A Treatise on Electricity and Magnetism” in 1873.¹¹

Heaviside’s importance is that he took these laws and equations to a whole new level. Heaviside’s “Electrical Papers” were compiled and published in 1892, but much of his work was performed long before this. One of his most profound observations in these papers can be found in Vol. 1, 1892, page 434 and 438, where wrote:

“By the way, is there such a thing as an electric current? Not that it is intended to cast any doubt upon the existence of a phenomenon so called; but is it a current – that is, something moving through a wire …[what if] we reverse this: the current in the wire is set up by the energy transmitted through the medium around it…“¹². Belrose paraphrases this as, “the real action lay not within conductors but in the field around them.”¹³ Heaviside was, of course, referring to transmission lines. His contributions to core and wire balun design, while indirect, are fundamental in nature. Although modern baluns were invented decades after his life, his mathematical theory for electromagnetic wave propagation still governs how these circuits operate today, as outlined below:

1. The fundamental equations for balun design come from Oliver Heaviside who first mathematically described circuit operation along a transmission line in an August 1876 paper, “On the Extra Current”.⁵ His model was the first to demonstrate electromagnetic wave reflection on a wire and wave patterns that form along a transmission line. “Originally developed to describe telegraph wires, the theory can also be applied to radio frequency conductors”.⁵ In light of the distributed capacitance and inductance that Heaviside described, it became clear that multiple wires could be wound together (e.g. bifilar) and these tightly-coupled windings would then act as a transmission line that perfectly balances the currents while maintaining equal and opposite voltages.
2. Heaviside invented the coaxial cable and patented it in England and was issued British Patent No. 1,407 on April 6, 1880. His inner conductor-insulating layer-outer shield construction confined the electromagnetic field, maintaining low loss and protecting the internal signal from external interference. This principle is the basis for all coax-based baluns, even the Guanella balun, one of the most compelling developments in RF component design of the 20^th century.¹⁴ On April 5, 1945, nearly 65 years to the day that Heaviside received his British coax patent, Swiss Radio Engineer Gustav Guanella filed for his coaxial transmission line balun patent.^15,16 Many high-permeability ferrite-based balun transformers designed today leverage Heaviside’s equations and Guanella’s awesome work. When discussing the Guanella balun, another article on the Mini-Circuits blog, RF transformer types, explains, “This 1:1 type of balun transformer creates a high choking reactance on the outer conductor of the coaxial cable, effectively reducing common mode signals while allowing the internal currents of the coaxial transmission line to pass unimpeded.”³
3. By reformulating Maxwell’s Equations between 1884 and 1885, Heaviside took 12 of James Clerk Maxwell’s original 20 complex equations and boiled them down into the four vector calculus equations now used in modern physics and RF engineering. By developing curl and divergence operators, which any electrical engineering student will study in an electromagnetic theory course today, he effectively allows engineers to model and compute not just the magnetic flux inside a magnetic (ferrite) core, but the leakage inductance between twisted wires.¹⁷
4. Heaviside’s work in defining energy flow between conductors fostered an understanding within the engineering community of common mode vs. differential mode currents.

This appendix would not be complete without quoting James C. Rautio, and in turn Heaviside himself, “I close with a paragraph written January 30, 1891 in Heaviside’s Electromagnetic Theory: ‘Lastly, from millions of vibrations per second, proceed to billions, and we come to light (and heat) radiation, which are, in Maxwell’s theory, identified with electromagnetic disturbances. The great gap between Hertzian waves and waves of light has not yet been bridged, but I do not doubt that it will be done by the discovery of improved methods of generating and observing very short waves.’

We truly do stand on the shoulders of giants.”¹⁸

References:

1. LTCC Filters Enhance Differential Circuit Designs – Mini-Circuits Blog
2. RF Transformer Fundamentals – Mini-Circuits Blog
3. Demystifying Transformers: Baluns and Ununs – Mini-Circuits Blog
4. Mini-Circuits – Transformers – AN20002.doc
5. Telegrapher’s equations – Wikipedia
6. Lexicon of Balun and Transformer Configurations – Mini-Circuits Blog
7. Schematic and Layout Recommendations for the GSPS ADC
8. The art of passive matching a high-speed ADC analog-input front end
9. DAC39RF12EVM, DAC39RF12 Evaluation Module User’s Guide
10. Darrigol, Olivier (2003). Electrodynamics from Ampère to Einstein. Oxford: Oxford University Press. pp. 4–6. ISBN 978-0-19-850593-8.
11. Ampère’s circuital law – Wikipedia
12. Oliver Heaviside – Oliver Heaviside
13. Belrose-MUL-2014-Vol2-Mar_Apr-005 Oliver Heaviside-a first rate oddity-sage in solitude.doc
14. “Understanding RF/Microwave Push-Pull Amplifier Design” ‹ Mini-Circuits Blog
15. Push-Pull circuits and Wideband Transformers, SEMELAB PLC, Push-Pull Transistors (rf-design.co.za)
16. G. Guanella; “Novel Matching Systems for High Frequencies”; Brown-Boveri Review Sept 1944
17. Oliver Heaviside – Wikipedia
18. Twenty Three Years: The Acceptance of Maxwell’s Theory | Microwave Journal
19. Hunt, Bruce J. (2005). The Maxwellians. Ithaca, NY, USA: Cornell University Press. pp. 66–67. ISBN 0-80148234-8.