*TECHNICAL NOTE TN0026*

*Characterization of rf test probes*

*AlphaTest Corporation* supplies small diameter and short length test probes for use in testing electronic devices and packages.
The purpose of the small dimension probes is twofold: First, package configurations often require 0,5 mm (or closer) spacing
of electrical test contacts; Second at the rf frequencies involved in testing wireless technology (such as Bluetooth® technology)
and other telecommunication, radar, and sensor devices the signals would be attenuated and/or distorted by conventional test
probes.

*RF Applications* require a temporary test connection which is electrically invisible or at least electrically nonintrusive. Ideally
the contact would have compliance and zero length. Since that is itself a contradiction, the next best combination is* just enough
*compliance and* little* length. The problem with length is that it introduces some series inductance, capacitance, resistance and
some signal delay.

Probe characterization might be simpler if the probe were the whole story. In fact, the probe is probably the major detractor
from good test performance but the socket design and the test pad placement on the *device under test *can influence the outcome.
For example, the probe impedance is determined by the probe diameter, length and material and by the dielectric material in the
socket and by the distance to signal-ground and by the shape of signal-ground. Consequently, a probe with 20 milliohms of
series resistance may have a characteristic impedance of 50 Ohms when installed in the test socket ... not because the probe is
a 50 Ohm probe but rather because the geometries and the dielectric constants make it so.

Probe performance may vary from one part of the socket to another. That will happen because the characteristic impedance
of the #x probe installed *near a ground* will differ from the characteristic impedance of one installed* far from ground*.
Consequently one probe will provide a wider bandwidth, one a lower crosstalk, and one a better impedance match to the load.
Short of installing coaxial probes at every signal location in the socket, this distressing fact will remain. Fortunately, this is a
well understood condition and most of the rf devices will provide some control over this in their *signal* and *ground* pad locations.

DC characteristics include probe resistance which directly contributes to insertion loss in dc, lf, and rf tests.

*LF characteristics* will include resistance and inductance. The resistance will change (from the dc value) due to* skin effect *as
the current travels more to the outside of the conductor. In fact, this change in conductivity may be small compared to the
change in contact resistance from probe to probe or even from test to test. Again the compliant, temporary contact (test probe)
becomes the culprit. Series inductance becomes a contributor to the probe characteristics at low frequencies and a significant
contributor at rf frequencies. The inductance of the test probe can be compared to that of a short wire. While most inductance
formulas apply to coils, transformers, twisted pairs and long wires the inductance of a short wire can be calculated by an
accepted formula
^{&}
. The rule of thumb tells that the inductance of an interconnection, wire bond, or short wire is about 1 nH
per mm. A more rigorous calculation can be applied. If the length >> radius, Inductance_{DC} = 2•len [ln(2•len/r)-0.75] nH,
where

where Inductance_{DC} = low frequency inductance (excluding skin effects) and

len = length in cm, r = radius, and ln() is the natural logarithm.

or Inductance_{AC} = 2•len [ln(2•len/r)-1] nH,

where Inductance_{AC} is the external inductance of the wire or the inductance considering skin effects.

RF characteristics largely depend upon the probe inductance, so lets look further at this calculated inductance of the typical rf test probe. With lengths of 2 to 3 mm and diameters of 0,2 to 0,4 mm these will not have the >20:1 ratio of length to radius needed to use the simplified formula. The more fundamental formula can be applied.

Inductance_{AC} = 2•10^{-7} [len • ln{ len • (len^{2} + r^{2})^{½}/r} - (len^{2} + r^{2})^{½} + r] Henries,

where len = length in meters, r = radius, ln() is the natural logarithm and Inductance_{AC} is the Inductance in Henries. The ac
inductance is also referred to as the external inductance since it ignores the inductive effect of current flowing down the core
of the conductor.

Let us look at some small test probes:

Length/Diameter |
0,20 mm |
0,25 mm |
0,30 mm |
0,35 mm |
0,4 mm |

3,0 mm |
1.88 nH |
1.75 nH |
1.7 nH |
1.56 nH |
1.48 nH |

2,5 mm |
1.48 nH |
1.37 nH |
1.28 nH |
1.21 nH |
1.15 nH |

2,0 mm |
1.1 nH |
1.01 nH |
0.94 nH |
0.87 nH |
0.84 nH |

Simulated transmission characteristics can be produced using capacitance matrix extractors and spice simulation. In this approach, the dielectric, probe dimensions and conductivity, and probe placement can be included in the transmission line structure. That lets us look at the probe behavior as installed in a given socket. The socket can be analyzed for sinusoidal and pulsed input responses. This analysis provides bandwidth, crosstalk, and attenuation data on real and imaginary planes.

TDR measurements on sample sockets can provide measurements of overshoot, delay time, rise time, and amplitude. This data can be used to calculate impedance, attenuation, crosstalk, and reactance.

Network analysis of sample sockets can provide swept measurement data. Provided that the test equipment is connected perfectly and that the sensor probes are perfect, this data can provide bandwidth, crosstalk, and reflection data in real & imaginary planes at finite test probe positions. The data can be translated into other formats. Remember that there is some margin of error in the connection of instrumentation to the socket under test and in the conversion of data to other forms.

Limits exist. No probe can be better than the basic mathematics (calculation) indicates. If its geometry indicates that it has over
a nH of inductance, then question any data which claims a half nH. Socket performance can be evaluated with measurement
equipment with the capability of showing results in several formats. This requires great care in the mechanics of the
measurement (mostly in the connection of the test equipment to the socket) and competency in the interpretation and translation
of the data. Finally, the socket must perform in an imperfect test environment. We can strive to correctly characterize the socket
and only hope that the test engineer can apply it to his task so that the test reveals more about the *Device Under Test *than about
the interface and the test socket.

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