Skin effect in semiconductor
wires:
So far, we have considered the
resistance of a semiconductor wire to be linear and constant. This is
definitely the case for most semiconductor circuits. At very high frequencies however,
an additional phenomenon called the skin effect comes into play such that
the resistance becomes frequency-dependent.
High-frequency currents tend to
flow primarily on the surface of a conductor with the current density falling
off exponentially with depth into the conductor. The skin depth d is defined as
the depth where the current falls off to a value of e -1 of its nominal value,
and is given by
with f the frequency of the
signal and U the permeability of the surrounding dielectric (typically equal to
the permeability of free space, or m = 4p ´ 10-7 H/m). For Aluminum at 1 GHz,
the skin depth is equal to 2.6 mm.
The obvious question is now if
this is something we should be concerned about when designing state-of-the-art
digital circuits?
The effect can be approximated by
assuming that the current flows uniformly in an outer shell of the conductor
with thickness d, as is illustrated in Figure for a rectangular wire.
Assuming that the overall cross-section of the wire is now limited to approximately
we obtain the following expression for the resistance (per unit
length) at high frequencies (f > fs):
The increased resistance at
higher frequencies may cause an extra attenuation and hence distortion of
the signal being transmitted over the wire. To determine the on-set of the
skin-effect, we can find the frequency fs where the skin depth is equal to half
the largest dimension (W or H) of the conductor. Below fs the whole wire is
conducting current, and the resistance is equal to (constant) low-frequency
resistance of the wire. From Eq. (4.6), we find the value of fs:
I have long felt a special connection with herbal medicine. First, it's natural, Charlie attended the same small college in Southern California - Claremont Men's College - although he dropped out of school to enroll in the Julliard School of Performing Arts in New York. York. Had he been to Claremont, he would have been senior the year I started there; I often thought that was the reason he was gone when he discovered that I had herpes. So, my life was lonely, all day, I could not stand the pain of the outbreak, and then Tasha introduced me to Dr. Itua who uses her herbal medicines to cure her two weeks of consumption. I place an order for him and he hands it to my post office, then I pick it up and use it for two weeks. All my wound is completely healed no more epidemic. I tell you honestly that this man is a great man, I trust him Herbal medicine so much that I share this to show my gratitude and also to let sick people know that there is hope with Dr. Itua. Herbal Phytotherapy.Dr Itua Contact Email.drituaherbalcenter@gmail.com/Whatsapp ... 2348149277967
ReplyDeleteHe cures.
Herpes,
Prostate
Breast Cancer
Brain Cancer
CEREBRAL VASCULAR ACCIDENT.
,Endomertil Cancer, cerebrovascular diseases
Hepatitis,Glaucoma., Cataracts,Macular degeneration,Cardiovascular disease,Lung disease.Enlarged prostate,Osteoporosis.Alzheimer's disease,
Dementia.Tach Disease,Shingles,
Lung Cancer, Leukemia Lymphoma Cancer,
Lung Mesothelioma Asbestos,
Ovarian Cervical Uterine Cancer,
Skin Cancer, Brain Tumor,
H.P.V TYPE 1 TYPE 2 TYPE 3 AND TYPE 4. TYPE 5.
HIV,Arthritis,Amyotrophic Lateral Scoliosis,Fibromyalgia,Fluoroquinolone Toxicity
Cervical Cancer
Colo-rectal Cancer
Blood Cancer
SYPHILIS.
Diabetes
Liver / Inflammatory kidney
Epilepsy