Received: from RAPARIALAP1002 (dh03.s2.bnl.gov [130.199.2.243]) by exchange02.bnl.gov with SMTP (Microsoft Exchange Internet Mail Service Version 5.5.2656.59) id ZXR4QPL2; Mon, 27 Jan 2003 14:48:35 -0500 Message-ID: <01c401c2c63d$0bfe6000$f302c782@RAPARIALAP1002> Reply-To: "deepak raparia" From: "deepak raparia" To: "deepak raparia" Subject: Fw: Fits to the Exponential Drop Runs Date: Mon, 27 Jan 2003 14:48:21 -0500 Organization: BNL MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_01C0_01C2C613.22F5D650" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1106 Disposition-Notification-To: "deepak raparia" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 This is a multi-part message in MIME format. ------=_NextPart_000_01C0_01C2C613.22F5D650 Content-Type: multipart/alternative; boundary="----=_NextPart_001_01C1_01C2C613.22F5D650" ------=_NextPart_001_01C1_01C2C613.22F5D650 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable =20 ----- Original Message -----=20 From: Richard Thomas =20 To: Raparia, Deepak ; yylee@bnl.gov =20 Sent: Friday, January 10, 2003 4:58 PM Subject: Fits to the Exponential Drop Runs Dear Deepak and Y.Y., =20 The attached Excel workbook contains fits to exponential drop runs for tau values of 0.2, 0.25, 0.3, 0.4, and 0.5 ms. =20 The measured Vref signals were truly exponential, so it is easy to get = a good fit as long as one stays out of the noise at the end. =20 The Im signals however, aren't truly exponential at the start, and then there is some problem at the end also, so one has to select a range of measured current values over which to perform the fits. =20 The four-parameter fits for Vref are the fit using the model: If (t + td) < 0 Then Vref =3D Vref_max Else Vref =3D Vref_min + (Vref_max - Vref_min) * Exp (- (t + td) / tau ) End if All times are in milliseconds. [A mathematically identical equation = was used to generate the data samples loaded into the DAC to produce the down ramp.] td is the delay between the first value in the data set until the down ramp starts. (It is a negative number in the fit, and is just the zero offset of the time axis for the exponential drop. For the summary worksheet, I show the value as a positive number.) Vref_max is the maximum reference voltage at the flat top before the drop starts. Vref_min is the minimum reference voltage that would be reached after many tau. (Actually, after 7 tau, the programmed ramp was set to 0 V, but there could be small offsets in the DAC.) I used Solver to change the cells containing Vref_max, Vref_min, td, = and tau, so that the sum of the squares of the errors between the = calculated values and the measured values was minimized.=20 =20 The summary page shows the fit parameters based on 140 A/V for the PS reference signal. =20 For Im, only the data points in the middle of the down ramp could be modeled by an exponential drop, so I didn't need the IF statement in = the model. The individual run pages show the range of values used for each fit. The model equation was: Im =3D Im_min + (Im_max - Im_min) * Exp (- (t + td) / tau ) According to the DCCT used, the PS puts out about 13 A when Vref is 0. To find the offset for the Ln(Im) plots, a straight line was fit to Ln(Im - Ioffset) vs. Time. =20 =20 In selecting the points for the fit (using the Excel array formula LINEST) only those points that appeared visually to fall on a straight line were used. The fit is first performed with Ioffset set to 13 A. Then I used Solver to minimize the residual sum of squares of the fit = by changing the value in the cell for Ioffset. (As Solver changes = Ioffset, the values in the cells of the LINEST array formula change also.) If the values in the fit region really should fall on a straight line, = this is equivalent to finding the value of the offset that made the line as straight as possible for the values used in the fit. For example, on the worksheet labeled "0.2 ms", the Solver cell that contains the value to be minimized is K114, the residual sum of squares for the LINEST array formula, and the cell that is changed to minimize K114 is the value in cell G102 (Ioffset). [Cells J110:K114 contain the array formula for fitting a straight line to the Ln(Im-Ioff) values in cells C115:C177.] td for Im differs from the td for Vref by about 0.15 ms, so there is a lag of about 0.15 ms between the control voltage and the measured PS output. Richard Thomas =20 ------=_NextPart_001_01C1_01C2C613.22F5D650 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
 
----- Original Message -----=20
From: Richard = Thomas
Sent: Friday, January 10, 2003 4:58 PM
Subject: Fits to the Exponential Drop Runs

Dear Deepak and Y.Y.,
 
The attached Excel workbook contains = fits to=20 exponential drop runs for  tau  values of 0.2, 0.25, 0.3, = 0.4, and 0.5=20 ms.
 
The measured Vref signals were truly = exponential,=20 so it is easy to get a good fit as long as one stays out of the noise = at the=20 end.
 
The Im signals however, aren't truly = exponential at=20 the start, and then there is some problem at the end also, so one has = to select=20 a range of measured current values over which to perform the=20 fits.
 
The=20 four-parameter fits for Vref are the fit using the model:

If (t = + td)=20 < 0 Then
   Vref =3D Vref_max
Else
  Vref = =3D =20 Vref_min + (Vref_max - Vref_min) * Exp (- (t + td) / tau )
End=20 if
All times are in milliseconds.  [A mathematically identical = equation=20 was used to generate the data samples loaded into the DAC to produce = the down=20 ramp.]

td is the delay between the first value in the data set = until the=20 down ramp starts.  (It is a negative number in the fit, and is = just the=20 zero offset of the time axis for the exponential drop.  For the = summary=20 worksheet, I show the value as a positive number.)

Vref_max is = the=20 maximum reference voltage at the flat top before the drop=20 starts.

Vref_min is the minimum reference voltage that would be = reached=20 after many tau.  (Actually, after 7 tau, the programmed ramp was = set to 0=20 V, but there could be small offsets in the DAC.)

I used Solver = to change=20 the cells containing Vref_max, Vref_min, td, and tau, so that the sum = of the=20 squares of the errors between the calculated values and the measured = values was=20 minimized. 
 
The summary page shows the fit = parameters based on=20 140 A/V for the PS reference signal.
 
For Im, only=20 the data points in the middle of the down ramp could be modeled by an=20 exponential drop, so I didn't need the IF statement in the model.  = The=20 individual run pages show the range of values used for each fit. The = model=20 equation was:

  Im =3D  Im_min + (Im_max - Im_min) * = Exp (- (t +=20 td) / tau )
According to=20 the DCCT used, the PS puts out about 13 A when Vref is 0. To find the = offset for=20 the Ln(Im) plots, a straight line was fit to Ln(Im - Ioffset) vs.=20 Time. 
 
In selecting=20 the points for the fit (using the Excel array formula LINEST) only = those points=20 that appeared visually to fall on a straight line were used.  The = fit is=20 first performed with Ioffset set to 13 A.  Then I used Solver to = minimize=20 the residual sum of squares of the fit by changing the value in the = cell for=20 Ioffset.  (As Solver changes Ioffset, the values in the cells of = the=20 LINEST array formula change also.)  If the values in the = fit=20 region really should fall on a straight line, this is equivalent = to finding=20 the value of the offset that made the line as straight as possible for = the=20 values used in the fit.

For=20 example, on the worksheet labeled "0.2 ms", the Solver cell that = contains the=20 value to be minimized is K114, the residual sum of squares for the = LINEST array=20 formula, and the cell that is changed to minimize K114 is the
value = in cell=20 G102 (Ioffset).  [Cells J110:K114 contain the array formula for = fitting a=20 straight line to the Ln(Im-Ioff) values in cells=20 C115:C177.]
td for Im=20 differs from the td for Vref by about 0.15 ms, so there is a lag of = about 0.15=20 ms between the control voltage and the measured PS=20 output.
Richard Thomas
 
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