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# 4.4 Extracted Device Quantities: Invariants

The well known definition for the current gain cut-off frequency is given in (4.10). (4.10)

This definition of has various approximations in terms of intrinsic small-signal equivalent elements. The most important approximations for a HEMT are (assuming the parasitic inductances and capacitances to be stripped off) according to Baeyens in : (4.11)

and even simpler in (4.12) neglecting the parasitic resistances and the output conductance: (4.12)

On the contrary, the inclusion of the pad capacities and the fringe part from (4.4) in (4.11) yield an extrinsic charging time and extrinsic , respectively. (4.13)

The intrinsic transconductance and the extrinsic transconductance are then related by: (4.14)

where is the extrinsic output conductance. Using (4.11)-(4.13) is precisely defined for different levels of deembedding.

The quantity is defined in several manners depending on the invariants used for its definition . Defining the Unilateral Power Gain allows for the highest values of in a device representing the maximum gain in a lossless reciprocal deembedding . (4.15)

Second, the Maximum Available Gain (MAG) and the Maximum Stable Gain (MSG) can be used for defining : (4.16)

for the stability factor  1. is then determined as: (4.17)

The MAG drops with a slope of -20 dB/dec as a function of frequency near =1. Kurokawa's stability factor is defined from the S-parameters as : (4.18)

The Maximum Stable Gain (MSG) is used for  1 is defined as: (4.19)

The MSG drops with -10 dB/dec as a function of frequency. The transition between the two for = 1 defines the frequency , from which based on MAG/MSG eventually can be extrapolated with a slope of -20 dB/dec for a given gate width . The frequency: (4.20)

defines the stability point and is expressed as a function of small-signal elements . depends the single finger gate width and is a critical quantity for amplifier design, especially for mm-wave applications. It will be analyzed in Chapter 7 with respect to statistical changes of mm-wave devices.   Next: 4.5 Interface to a Up: 4. RF-Extraction Previous: 4.3 Application Example
Quay
2001-12-21