Re: TI-92 Phasor
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Regarding the TI-92 phasor anomaly, I've sent the following reply to
Peter at ti-cares@ti.com. If any of you electrical engineering types
agree there is a problem you might want to send a note to them.
Peter,
Thank you for the explanation of why the calculator performs as it does.
I had assumed that the degree/radian mismatch was the problem and in
general agree with you regarding the use of degrees in exponential form,
There is, however, a field in electrical engineering that uses polar
notation in degree form (phasors). AC circuit analysis (pioneered by
Charles Steinmetz) expresses magnitude and phase of AC (alternating
current) electrical circuits in any of three notations:
polar - V (degree symbol) theta
rectangular - V cos theta + i V sin theta
exponential - V e^i theta
V = voltage
(degree symbol) = degree angle symbol (SHIFT D on TI-92 keyboard)
theta = theta angle in degrees
the relationship between the notations is established by Euler's
identity:
e^i theta = cos theta + i sin theta
Without getting into details the various notations are used when
manipulating parameters in parallel/serial circuits. Consult any ac
electrical engineering book for a more thorough discussion. Depending on
the variables, polar to rectangular conversions may have to be tediously
performed several times to arrive at the final solution. When matrices
are involved, more time is spent performing conversions than solving
problems. My use of degrees in exponential notation (Euler's identity)
was an attempt to overcome this difficulty.
Nevertheless, I think there is a limitation in the TI-92 regarding polar
complex notation, that should be corrected or identified. In the
meantime I shall write a program that provides a workaround.
Warmest regards,
Randall R Vogtman
>In DEGREE mode, the TI-92 scales the arguments of trig functions by pi/180,
and
>does not scale the arguments of the other built-in functions, such as the
>exponential and logarithmic functions. It does not scale the arguments of the
>exp and log functions because, mathematically, there is no angle measure
(radian
>or degree) associated with those functions. As a consequence of this,
>calculations involving polar complex numbers in DEGREE mode violate the
>fundamental complex identity cos(x) + i*sin(x) = e^(i*x). Combining complex
>functions with DEGREE mode can, therefore, lead to very confusing results.
>
>When defining x=e^(70.*i), 70 is not handled as 70 degrees. If you input
>e^(70.*i)->x, you will notice it is displayed on the right side as
e^(50.7E0*i).
>If you convert 70 radians you get 4010.7 degrees. Converting this to a
primary
>angle gives. 50.7 degrees. If you then type x and press enter, you will see
>e^(25.1576E0i). This is the primary angle of 50.7 radians converted to
degrees.
>
>When you do not enter the decimal point, assuming that you are in AUTO mode,
>you are not asking the TI-92 for an exact answer so it does not perform any
>calculation yet.
>
>You can see why the TI-92 would not automatically scale the arguments of the
>exponential function in DEGREE mode: you would be surprised if you computed
e^1, but
>were unknowingly in DEGREE mode... rather than seeing the expected e (~2.718),
>you saw e^(1*pi/180) (~1.018). Therefore, you need to stay in RADIAN mode
when
>working with complex number calculations.
>
>I hope you find this information helpful. If you have any further questions
or
>comments, please feel free to contact us again.
>
>Best Regards,
>Peter
>------------------------------------------------------------
>TI Consumer Relations Internet:ti-cares@ti.com
>Texas Instruments Phone:(817)774-6827
>P.O. Box 6118 m/s 3268 Fax:(817)774-6074
>Temple, TX 76503
>------------------------------------------------------------
>
>------------------
>Original text
>
>From: shamaal@iwl.net (Randall R Vogtman), on 10/22/96 9:56 PM:
>To: ti-cares@ti.com
>Cc: rvogtman@ssf6.jsc.nasa.gov
>
>Dear TI-cares,
>
>While performing phasor analysis on my TI-92 I noticed the following problem:
>
>First I input the following sequence:
>
> 70.*i
>Define x=e
>
>(the i is imaginary)
>
>Next I press x to verify and the following is returned:
>
> 25.1576E0i
>e
>
>This is not what I input. When I perform the define command without the
>decimal point, that is:
>
> 70*i
>Define x=e
>
>I receive the correct value when x is returned.
>
>I discovered this while performing rudimentary phasor calculations, and it
>has proved to be inconvenient.
>
>Please advise if there is a workaround or a misunderstanding on my part.
>
>Randall R Vogtman
References: