When broadband signals are transmitted on lines of any significant length, impedance discontinuities or mismatches degrade the amplitude and phase accuracy, as well as the temporal fidelity, of waveforms generated with a signal generator. To minimize signal reflections, the source and load impedances should equal the characteristic impedance of the transmission line.

One of the most common mismatch errors encountered in such measurements is shown in the following figure:

Figure 6. Common Mismatch Measurement Error


In this example, selectable source impedances are provided at the signal generator outputs to accommodate the most popular coaxial cable characteristic impedances: 50 Ω and 75 Ω.

Consider an example where a 50 Ω coaxial cable connects 75 Ω source and load impedances. The following figure shows the discontinuities that occur in this situation and how they compare to a matched cable:

Figure 7. Discontinuities Caused by Mismatched Cable


The pulse encounters impedance mismatches at each end of the cable, and the pulse is partially reflected. The reflected pulse traverses the cable back and forth numerous times, diminishing at each end by the reflection coefficient, Γ:

Γ = v r v i = z t − z 0 z t + z 0

where

  • vr = reflected voltage
  • vi = incident voltage
  • zt = terminating impedance
  • z0 = characteristic impedance

The resulting voltage waveform is distorted by the asymptotic decay of the reflected pulse as shown, exaggerated for visual effect. Impedance discontinuities of smaller magnitude and/or duration have correspondingly smaller effects. Also displayed is the waveform that results when a cable of matched impedance (75 Ω) is used.

Mismatch Uncertainty

Impedance matching is also important for preserving the absolute delivered power from a device. The accuracy with which power can be delivered is limited by mismatch error. The mismatch error in a z0 system can be shown to be bounded by:

( 1 − | Γ L | 2 ) ( 1 + | Γ L | ⋅ | Γ G | ) 2 ≤ mismatch error ≤ ( 1 − | Γ L | 2 ) ( 1 − | Γ L | ⋅ | Γ G | ) 2

where

  • ΓL = load reflection coefficient
  • ΓG = generator reflection coefficient

The denominator term represents mismatch uncertainty, which is a fundamental limit to the power transfer accuracy that can be achieved across a mismatched junction.

Resistive Matching

You can use a resistor in series (shunt) to match the total source impedance (admittance) that an RF signal generator sees to the characteristic impedance (admittance) of a cable. This method works for RF signal generates with low or high source impedance.

RF signal generators that are not capable of driving the cable impedance directly can be coupled through a matching L-pad. In this case, the RF signal generator sees an approximately 500 Ω load, while the source impedance presented to the cable is 50 Ω.

Refer to the following figure:

Figure 8. Coupling RF Signal Generators Using an L-Pad


To minimize parasitic effects, use high-frequency components and layout techniques throughout.