**Wideband transformers used in ADC and RF applications**

Within the huge range of wideband transformers, there are selections on passband frequency, turns ratios, and pin configurations. **Figure 1** shows an example configuration range from a typical industry sample kit (Ref. 1).

**Figure 1**

The two most commonly used in ADC input interfaces are No. 1 and No. 3 above. The second one is very similar to No. 1, but the selection range seems much larger with the secondary centertap. Configurations No. 1 and No. 2 are often called “flux-coupled baluns,” which is not particularly descriptive, as all configurations of **Figure 1** have to be flux coupled to operate.

Configuration No. 3 is also very common and typically aimed at higher-frequency applications. Configuration No. 3 is often referred to as a “transmission line transformer” but is also called a common mode choke. It can also deliver a “Balun, Balanced to Unbalanced” operation — or more commonly unbalanced to balanced in single-ended input to ADC differential input interfaces common to ADC evaluation boards (Ref. 2).

The focus here will be on baluns of configuration No. 1 (or equivalently, No. 2). While this shows a secondary centertap, it is perfectly acceptable to not use that connection, and that will be the assumption here. Floating the centertap in the configurations shown later will remove the gain and phase balance concerns typical of that configuration.

Transformer vendors use many different approaches to describing their operations. All, however, will report insertion loss or bandwidth specifications assuming some source impedance. In RF applications, those specifications are normally assuming the secondary is terminated in an impedance that is n^{2} *Rs. This doubly terminated assumption gives some point of comparison between devices, but, in fact, transformers will give some level of operation and passband response with a huge range of source and load impedances. Any Spice modeling approach should track that physical reality but probably start with the doubly terminated assumption for measurement purposes.

**Network analyzer balun measurements and coupled inductor model element solution**

Typical lab network analyzers can easily make an S21 transmission measurement. For best results, the device under test (DUT) input and output impedance should be 50Ω. **Figure 2** shows the measurement setup for a wideband 1:2 ohms (or 1:1.414 turns) ratio transformer (Ref. 3).

**Figure 2**

After calibration, the network analyzer simply drives into the blocking caps and then into the primary of the transformer. If the secondary load impedance is set to n^{2} *Rs, it will appear on the input side of the transformer as an Rs termination, eliminating any line reflection effects. However, the test schematic of **Figure 2** should also translate to a source impedance on the output side of the board matched to the network analyzer measurement impedance — most commonly 50Ω.

The exact solution for those impedance mapping elements (R1 & R2) gives 70.7Ω where those shown in **Figure 2** are close 1 percent values. R1 and R2 are solved to give an impedance looking out of the balun secondary equal to n^{2} *Rs (100Ω here) while also presenting a 50Ω source looking back into R2. Those exact solutions are shown here where “n” is the turns' ratio.

Using these exact values will give an anticipated measured midband insertion loss for this test circuit as:

Using an exact n=√2 and Rs=50Ω produces R1=R2=70.71Ω. The simulation of **Figure 1** , using a source increased to “2” to account for the calibration and the 69.8 nominal 1 percent values, will give the expected midband insertion loss (Ref. 4) of -7.85dB (vs an ideal of -7.65dB evaluating eq. 3). Any measured loss exceeding this can be interpreted as the midband insertion loss for the transformer giving a transfer gain slightly lower than ideal.

Building **Figure 2** for measurement purposes gave the test board of **Figure 3** .

**Figure 3**

One of the difficulties in extracting a model for wideband baluns is getting both the high and low f_{-3dB} frequencies. For the low-frequency side, the HP4195 offers a nice frequency span for this measurement. That measurement is shown in **Figure 4** on a very fine 0.5dB/div scale.

**Figure 4**

This 10kHz to 500Mhz sweep pulls out the lower-frequency response nicely but is not especially useful on the high end. The low-frequency f_{-3dB} cutoff can be read from this measurement to be about 50kHz. The low-end -0.5dB limit was slightly lower than 200kHz, so it is difficult to interpret the 0.4Mhz from the ADT2-1T data sheet. It has normally been the case that measured results show a much lower passband frequency than typically indicated in balun data sheets. The upper -0.5dB rolloff is shown as the marker at 268Mhz but no high end f_{-3dB} can be extracted here.

To get a better read on the upper f_{-3dB} and midband insertion loss, the measurement was moved to an Agilent 4396A using a 100kHz to 1Ghz log sweep. That data can be downloaded into Excel then compared to simulation results. The ideal transformer model used in iSim PE is only looking for a primary inductance, turns ratio, and coupling coefficient. From the high (f_{H} ) and low (f_{L} ) f_{-3dB} frequencies, these are given by (Ref. 5):

The high-frequency f_{-3dB} measured f_{H} =825Mhz on the ADT2-1T gives the transformer model of **Figure 5** . The secondary inductance is always n^{2} *L_{1} .

**Figure 5**

The measured response on the ADT2-1T showed about 0.26dB more insertion loss midband vs the ideal model simulation. **Figure 6** shows the measured S21 data from 100kHz to 1Ghz, the nominal model generated by the elements of **Figure 5** put into **Figure 2** , and then the simulated data just shifted down by 0.26dB. The measured data shows a bit more low-frequency rolloff than a simple ideal model would predict, but relatively good fit is shown with the level shifted data from 1Mhz to 1GHz. This model will shift the gains and response shapes correctly when using any source and load impedance.

**Figure 6**

**Including the midband insertion loss in the model**

One approach to including the insertion loss (IL) in the model would be to insert some winding resistance in each of the transformer legs. That R_{w} term will be inserted on the primary, then n*R_{w} on the secondary for this step-up configuration. If the added insertion loss is converted to a linear gain and then used as shown here, a value for the primary winding resistance may be computed. This α term should be slightly lower than 1.0, so use a negative number for IL.

Then:

Adding a bit of winding resistance to the primary will change the low frequency cutoff if L_{1} is not modified. The approximate adjustment for that would be:

Making those adjustments in the iSim PE model gives the updated schematic of **Figure 7** , where the -0.26dB midband insertion loss computes to 1.77Ω on the primary and 2.51Ω on the secondary. The primary inductance was shifted up just slightly from 80uH to 82.8uH.

**Figure 7**

Running this simulation and putting that data on the plot of **Figure 6** gives the exact match shown in **Figure 8** . Using this winding resistance approach appears to be exactly equivalent to shifting the nominal model down by 0.26dB.

**Figure 8**

**Applying this improved Balun model to an ADC input driver circuit**

This more detailed balun modeling exercise is aimed at correctly predicting the flatness span using different combinations of baluns, amplifiers, and other external passive elements. One example would be the ISL55210 evaluation board implementation. This is intended to show the response for a balun coupled to a wideband fully differential amplifier (FDA) (Ref. 6). **Figure 9** shows the simulation circuit for this board. Normally, the output side of this circuit would feed into an ADC, but for independent testing of this part of the solution, an output balun was also used on this evaluation module (EVM) to get back to single-ended for the typical network and spectrum analyzer measurements intended with this circuit.

**Figure 9**

Here, the output circuit is showing 200Ω load to the FDA but 50Ω source to the 1:1 output balun, where that model has been adjusted to include 1.58Ω winding resistance and 81.93uH primary inductance with 0.99988 coupling coefficient, to correctly model its measured 43khz to 850Mhz f_{-3dB} bandwidths. Taking a 100kHz to 1GHz measurement of this board, and comparing to the simulation data from the circuit of **Figure 9** gives the very close match of **Figure 10** .

**Figure 10**

Having the separate pieces to the response shape allows the source of any response rolloffs to be identified. The midband gain is almost exactly matched by including the winding resistance. The high- and low-frequency rolloffs are modeled very closely where the slight deviation on the low side can be attributed to the ADT2-1T as shown in **Figure 6** . Having good confidence in the balun models allows the response to the FDA output pins to be generated via simulation, as shown in **Figure 11** . The measured 520Mhz high-frequency bandwidth of **Figure 10** is principally set by the transformer shapes with the available bandwidth up to the FDA output a much wider 800Mhz f_{-3dB} .

**Figure 11**

**Summary and conclusions**

Taking a very wideband balun measurement matching the impedances across the balun, but presenting a 50Ω match to the network analyzer, has allowed accurate hi/lo f_{-3dB} points to be measured. Using these in a simple coupled inductor model of a transformer has shown a model that will correctly adjust for different source and load elements in a Spice simulation. Adding winding resistance in each of the legs of the balun has proven an effective means to including insertion loss to the simulation model.

Combining these improved balun models with a good amplifier model has shown very close match from measured to simulated response shapes on a modern FDA evaluation board. Having each of the elements correctly modeled can provide a quick design tool across a broad range of intended configuration for this type of application. Using the modeling methodology detailed here can allow a wide range of baluns to be considered in these types of ADC interface circuits.

**References for measurement and modeling of wideband baluns**

1. M/A – Com 75Ω designer kit.

2. High frequency 12 to 14-bit ADC evaluation board, Figure 2.

3. The model here is a Mini-Circuits 1:2 Ohms ratio device specified in 50Ω to be 0.4 to 450MHz

4. These simulations are being done in Intersil’s free Spice and power simulator download. Registration required.

5. Contact the author for an article detailing this model: msteffes@intersil.com

6. Designer’s guide to the ISL55210 and ISL55211 evaluation boards

Interesting that the transformer–among the oldest electrical components–still finds so may roles. The induction principle was discovered in the 1830s, and the first commnercial transformers were used in the 1880s–but they were for power, not signal.

A properly designed and used transformer can be an extremely reliable device and a solution to a lot of problems in signal isolation, baluns (as this blog shows), power transfer, voltage/current step-up/down, impedance matching, and many others. Not bad for a “dumb”, passive part!

Sorry,I forgot to include the link to an interesting resource on their history:

http://edisontechcenter.org/Transformers.html

and there are many more you can find.

Of course, these transformers are rather more sophisticated that the ones that George Westinghouse and Charles Steinmetz were working with. Somewhat wider bandwidth and more predictable response with regard to common- and differential-mode behavior.