The approximate model in Fig 1 makes it easier to include high-frequency transformers in a Spice simulation. Broadband pulse transformers are widely used to transform impedance levels as a noise-reduction or source-matching technique. Fig 1 includes the physical model and the key performance equations. The model shows the transformer providing a voltage gain from V_S to V_O, an input impedance of R_L/n2, and an output impedance of n2R_S.

To simulate the transformer, the Spice simulation requires L₁, L₂, and k as inputs. However, transformer manufacturers typically specify only an impedance ratio (n2) and the two -3-dB frequencies of the transformer's bandpass response. If the passband is greater than two decades wide, which translates into k>0.98, the following Laplace bandpass transfer function approximates the frequency response for the model:

where the left denominator term determines the low-frequency cutoff of 2ãf_L and the right denominator term determines the high-frequency cutoff of 2ãf_H. Manufacturers usually specify the -3-dB frequencies, f_L and f_H, of broadband pulse transformers with R_S50ê and R_Ln2R_S. You can solve Eq 1 for the three required Spice model parameters as follows:

To illustrate how this model works, consider using a 1:4 transformer in front of a low-noise op amp to reduce its noise figure. The specifications for an RF Prime (Sacramento, CA, (916) 368-4400)) RFTM-16 transformer indicate an impedance ratio of 16 (n=4) and -3-dB frequencies of 30 kHz and 75 MHz. The three input parameters are as follows:

You can now use the transformer model along with the op amp's macromodel to develop a full simulation for the test circuit in Fig 2. This circuit provides a good 50ê input- and output-impedance match, a midband gain of +10 (20 dB) from the source to the matched load, and an input-noise figure that has been reduced from 9.5 dB for just the op amp to 4.2 dB with the input transformer.

Curve 1 in Fig 3 shows the response of the transformer only. With R_Tn2R_S, the circuit attenuates V_S by one-half to the input of the transformer and then provides a gain of n to the secondary side. The result is a net gain of +2 from the source to the input of the op amp. Curve 1 shows this midband gain and the correct low-frequency cutoff and also what appears to be second-order high-frequency roll-off. The op amp's input capacitance causes this roll-off, and removing the op amp shows exactly the desired 75-MHz single-pole roll-off for the transformer by itself. Curve 2 shows the response of the op amp alone. C_F intentionally bandlimits the op amp's response to reduce high-frequency noise at the output.

Curve 3 is the total response from the source to the load showing the desired 20-dB gain with approximately the same frequency response as the transformer.

Ed Note: The author thanks Paul Clark at RF Prime for his suggestion in applying high-frequency transformers and for verifying the simplified model shown here. (DI #1681)