Considerations for the Design of the Beam current Monitor System

**For the Spallation Neutron Source (SNS)**

**M. Kesselman**

# Rev1- March 5, 2002

The Spallation Neutron Source to be built at ORNL is comprised of a
source of H^-^ particles (FE), a medium energy beam transport (MEBT), a
linear accelerator (Linac), a high energy beam transport (HEBT), a
stripper changing the H^-^ to H^+^ and an accumulator ring (Ring), a
ring to target beam transport (RTBT), and a target. Current wave shapes
will vary at different places along the system. The source will generate
charge bunches that will have an amplitude near 50ma peak (38ma peak in
the MEBT,Linac, and HEBT), and bunch widths of 300ns to 645ns (defining
a mini-pulse). The bunches are repeated at the revolution period about
945ns. This provides a "gap" time of about 300ns used by the ring to
kick the beam out to the target. The pulses are accumulated by the ring
for 1ms (about 1060 mini-pulses) after which the entire ring is dumped
to the target. The process is repeated at a 60Hz rate. The 1 ms pulse
duration constitutes a "macro-pulse". An RF micro-structure of 402.5MHz
is generated by the accelerator RF.

The beam current will vary in amplitude from the near 50ma peak pulses
with a pulsing duration of 1ms (chopper rise time about 10ns) in the
MEBT, Linac and HEBT to a ramping pulsed current of near 50Amp peak and
duration of 1ms in the Ring, and about a 50Amp 645ns pulse in the RTBT.
This represents a dynamic range of 1000:1. Adding some resolution at the
low end easily exceeds this by a factor of about 100. It is desired to
provide a system capable of 1% accuracy with a resolution of 0.5%
(resolution was relaxed from 0.1% to 0.5% in the Ring and RTBT to avoid
excessive gain changing --see EMAIL from Fedotov 4/20/01).

**AP Requirements (3/2001):**

MEBT-to-HEBT:

Range 15mA -- 52mA

Accuracy 1%

Resolution 0.1%

Data Structure Inside mini-pulse

Comments \-\-\-\-\-\-\-\-\-\--

RING-RTBT:

Intensity 5E10 -- 2E14

Range 15mA -- 100A

Accuracy 1%

Resolution 0.1% resolution relaxed to 0.5%?

Data Structure Turn-by-turn

Comments All are Fast Current Transformers

**Desired capabilities of this system are:**

-   **a comfort display output,**

-   **calculation of average current and charge per macro-pulse,**

-   **calculation of average current and charge per mini-pulse,**

-   **ability to provide detailed signal wave shape of mini-pulse
    current and charge,**

-   **ability to permit detailed analysis of the mini-pulse (examine the
    chopper characteristics),**

-   **a representative analog version of each mini-pulse sent to the
    machine protection system (MPS).**

-   **ability to store a minimum of 10 macro-pulses of raw data in a
    circular buffer for analysis upon demand (goal is 1 seconds worth of
    data),**

-   **a self calibration capability**

-   **remote and local operation**

In an effort to try to find a common design the choice of current
transformer has been compromised to balance sensitivity for the lower
currents and droop for the longer duration macro-pulse. It is felt that
droop could be compensated using digital compensation techniques
justifying this approach. Such a technique and initial simulation
results will be presented later.

**OVERALL CHALLENGES:**

### Providing capability to analyze the chopper edge (10ns), and still provide accurate measurements for the longer 1ms macro-pulse (choice of transformer)

## Dealing with large dynamic range -- Gain change requirements with minimal loss of turn information

## Handling potentially large input voltages -- selection of components and component protection

-   **Computation accuracy/resolution and selection of ADC and sampling
    rate**

-   **Calibration pulse generator and techniques**

**Transformer selection:**

A number of approaches were considered before arriving at the Bergoz
FCT. The requirement to be able to analyze the edge of the mini-pulse
requires a rise time less than 0.3 times the pulse rise time (3ns) to
maintain a 10% rise time measurement. This is a bandwidth near
0.35/3\*10E-9 or 100MHz. A transformer rise time less than 1ns
(providing better than 1% measurement accuracy) was made a requirement.
It is also desirable to have less than 0.1% droop during the 1 ms
macro-pulse to maintain good pulse height accuracy. This requires a
transformer time constant (L/R) corner greater than 1000\*0.001s or \>1
second (lower cut-off frequency of \<0.159Hz). Thus, the transformer
that would meet these requirements would have a lower cut-off of
\<0.159Hz and an upper cut-off \>350MHz.

An initial attempt to design such a transformer achieved a lower cut-of
0.2Hz and upper cut-off at about 10MHz. This was abandoned, and an
alternate approach pursued. The concept of utilizing two or more
different transformers was addressed. This was undesirable from a
"common solution" point of view. The purchase of commercially available
current transformers capable of 1ns rise time focused on transformers of
the Bergoz FCT type. Such transformers could provide a good compromise
for sensitivity and droop for the short mini-pulse but suffered from
considerable droop for the macro-pulse (0.1%/μs). The requirement to
observe the rise time of the chopper was left to a fast digitizer/scope
type acquisition system, while the slower macro-pulse information was
addressed with a rise time near 50ns due to Ring beam dispersion after a
number of turns. Communications with Bergoz and others led us to
conclude that the FCT would work well in the high speed domain, while
digital compensation could restore the low frequency corner to near
0.16Hz.

Bergoz was approached to design a balanced transformer (100:1), capable
of driving a 78 Ohm balanced coaxial line. It was thought that such a
configuration would minimize noise pick-up along the long (100 m) cable.
The initial prototype transformer suffered from transient anomalies, and
the balanced line suffered from a limited choice of cables and large
losses at the higher frequencies. This concept was abandoned in favor of
a more conventional 50 Ohm transformer with many cables to choose from
to minimize cable distortion. A prototype transformer with 50:1 turns
ratio and an additional winding of 10 turns for calibration injection
was tested and performed well. This transformer provides a nominal 25 mV
signal for a 50mA input current (suffers about 0.5dB loss due to
internal resistors used to improve transient response and match the
transformer to the coax), \<1ns rise-time, and \<0.1%/μs droop. Success
with the prototype, an ability to obtain rad-hard transformers and an
excellent working relationship with Julian Bergoz has prompted us to
designate this transformer universally for the SNS. The MEBT has
installed two small diameter units that appear to be working well.

**The Digital Compensation Scheme:**

To utilize the FCT in our application it is necessary to provide DC
restoration and digital compensation of the transformer droop. An
algorithm to accomplish this has been tested and appears to work quite
well. It requires a good estimate of the transformer droop time constant
(0.16% error in droop time constant for 0.1% error in droop) and DC
restoration. The algorithm is based upon an IIR filter with a zero to
cancel the transformer low cut-off pole, and replacement of the
transformer low cut-off pole with a new pole at 0.159Hz. The DC
restoration requires a measurement of the DC level just prior to the
pulse. This is subtracted from the data set to restore the DC value to
zero. The concept requires some averaging of the data to achieve good
estimates of the offset and transformer droop time constant. This is
accomplished with numerous readings and least square estimate
calculations.

![](media/image1.wmf){width="5.138194444444444in"
height="2.9472222222222224in"}

![](media/image2.wmf){width="5.8381944444444445in"
height="4.216666666666667in"}

ie: H(s)= (s+1/τ~1~) / (s+1/τ~2~)

Where; 1/τ~1~ is the transformer lower cut-off radian frequency,

1/τ~2~ is the desired new transformer lower cut-off radian frequency

The Bilinear transform substitutes for s to obtain H(Z);

s= (2/T)\*(1-Z^-1^) / (1+Z^-1^)

Where; T is the sampling time interval

Yielding:

Y(n)={1/(2/T+1/τ~2~)}{y(n-1) (2/T-1/τ~2~) + x(n) (2/T +1/τ~1~) + x(n-1)
(-2/T +1/τ~1~)}

![](media/image3.wmf){width="5.4in" height="3.092361111111111in"}

![](media/image4.png){width="5.997916666666667in"
height="7.472222222222222in"}

A screen dump of LabVIEW code that acquires data from the BCM
electronics is shown above. Data was sampled at 40MHz, and only a short
section of the simulated burst was available in the 16K FIFO acquisition
board used to collect this data (a total of about 400us is stored and
displayed). Another acquisition board received later with 64K FIFOs was
capable of storing some zero offset data (about 50 uS, 2000 points), the
calibration pulse (about 250uS, about 10000 points), the 1 millisecond
burst (40000 points) and some of the recovery "tail" for analysis of
time constant. Of particular interest is the ability to make slight
adjustments to the droop compensation. This permitted very careful
adjustments to be made, and by inserting a calibration pulse just prior
to the simulated beam burst, the droop is calculated on the relatively
large calibration pulse.

It has been observed that very small differences in compensated DC level
are observable between the start and end of the macro-pulse when setting
the compensation to the time constant calculated from the calibration
pulse. A slightly different time constant is calculated when using the
tail of the burst response (burst=0.001111, cal=0.0011376). The best
response is obtained by using the "tail". It is felt that there is a
slight calibration pulse time constant that we are seeing. This may be
due to cable distortion, the pulse generator, or a DC offset error. This
brings to light some subtle things that could cause slight compensation
errors. The response of the cable to the signal during the tail is also
a consideration, and since there is a difference in calculated time
constants this affect would exist in both cases, and is not thought to
be the main cause for the difference. DC offset errors and pulse shape
are more likely at the root of the discrepancy. DC offset measurements
based upon a 1900 point average yielded changing offset answers from
run-to-run (-156 +/- 20 counts). A more careful investigation of this
revealed a ground loop problem between the calibration pulse generator
and the transformer ground. Just touching the grounds together produced
a DC offset change in the output of the electronics. Grounding the cable
shield to the electronics directly provides no change in offset. With
the calibration pulse generator removed, DC offset calculations varied
only --246 +/- 0.2 counts for a 1900 point average (note shift in
offset). The calculation of transformer droop time constant varied about
0.001103 +/- 0.000002. The final version of transformer ordered for this
system was requested with isolated calibration windings, permitting
measurement of current into this winding on the return line, and
avoiding a ground loop problem.

Using a calibration pulse before the beam arrives is advantageous due to
the fact that this is the more quiet time. The more accurate
calculation, it seems, is made during the beam tail, however, this could
be during a relatively noisy time (after the kicker etc.). The software
has been written to permit adequate control to set the desired window
for this calculation. In addition, small changes could be made to the
compensation time constant to achieve the droop desired.

**Cable Distortion:**

A Mathcad analysis was performed using parameters of a ¼ inch Heliax
Cable #456 to estimate the affect of distortion on a step input. The
results are shown in the figures below comparing 1/4", 3/8", and ½"
Heliax.

![](media/image5.wmf){width="4.65in" height="4.017361111111111in"}

![](media/image7.wmf){width="4.8in" height="4.118055555555555in"}

![](media/image8.wmf){width="5.0in" height="4.290277777777778in"}

![](media/image9.wmf){width="4.7in" height="3.9604166666666667in"}

![](media/image10.wmf){width="4.75in" height="4.002777777777778in"}

The response to a step for the ¼ inch Heliax indicates that the signal
is in error of about 3% after 300ns and 1.6% after 1us. Therefore, there
will exist an error in accuracy that must be corrected during the
calibration cycle. One can see from the plots above that the 3/8 inch
Heliax and ½ inch Heliax have improved transient response. The 3/8 inch
providing 1% error at 1us, and the ½ inch 0.5% at 1us. The rise times
also improve, with the time to 90% of 22.25ns for the ¼ inch, 16.075ns
for 3/8 inch and 6.73ns for ½ inch. Based upon this analysis, the 3/8
inch Heliax is a preferred choice since the rise time is near 1/3 the
rise time of the 7MHz filtering.

In addition, the response exhibits a slope that will modify the droop
response during calculation of the droop time constant. To examine more
closely this effect, the analysis was expanded to include up to 10us and
the axes were scaled to measure the slope. It was found that the
amplitude was 0.99527 and the slope 2.6E-4/us (0.026%/us). Therefore
waiting for 10us before performing a calculation of droop time constant
should provide sufficient time for the cable to stabilize sufficiently
for accurate calculation of time constant.

**Bandwidth, and Filter consideration:**

There are two signal bandwidths to consider. To examine the chopper
edges, a bandwidth in excess of 100MHz is required. This is expected to
be done by a separate high speed digitizing system like a scope. The
second requirement is to analyze the general shape of the mini-pulse and
macro-pulse. The system will be capable of following the mini-pulse,
however, due to beam dispersion after a number of turns in the ring, the
edge is expected to deteriorate to near a 50ns rise-time. To observe
this a bandwidth of about 0.35/50E-9 = 7MHz is required. Therefore, a
7MHz Gaussian filter will shape the signal before it goes to the ADC.
This will limit the noise bandwidth and provide a system response that
suffers no overshoot. In addition, The response of the filter must
return to baseline between mini-pulses (300ns max). A 5 pole Gaussian
filter will return to baseline to within 0.1% in about 6 time constants
(use 6.2 for Gaussian). Therefore, the smallest bandwidth filter that
must be considered is about 6/2π(300E-9) = 3.2MHz. Such a filter has a
rise time (0.1 to 0.9) of about 2.12\*50ns = 106ns (use 2.135\*τ~c~ for
a Gaussian). The estimated rise time for a 7MHz Gaussian filter is
2.12\*22.7ns = 48ns ( Duration of impulse response and Rise time of 5
pole Gaussian was estimated from curves for impulse and step response in
Zverev, "Handbook of Filter Synthesis", Wiley 1967, pg. 406; the
Gaussian numbers in parenthesis were derived from a table of the
integral of the Gaussian distribution providing probability information
and the transform pair exp(-αt^2^)←→exp(-ω^2^/4α)\*√(π/ α) where
α=1/2σ^2^ and σ is the standard deviation). Resulting signal rise time
is expected to be sqrt(48\^2 +50\^2)=69ns.

The ADC sampling near 65MHz has a potential bandwidth of 32.5MHz
(preferably synchronized to the revolution frequency by operating at 4
times the reference clock frequency of about 16MHz), and since the
analog part of the ADC is wide-band for under sampling applications the
signal bandwidth should be limited. This is accomplished by the AD602
variable gain amplifier which has a bandwidth of 35MHz, and by placing a
5-pole 7MHz Gaussian filter just before the AD8138 ADC driver. The 5
pole Gaussian filter provides attenuation at 5\*f ~c~ (35MHz) of about
--43dB, the AD602 adds another --3dB for a total of about --46dB. At
about 8\*f ~c~ (65-7=58MHz) the signals are attenuated by about --68.3dB
(-63dB for the filter and --5.3 for the amplifier). This will attenuate
all aliased information in the passband of the filter by --66dB which
will cause corruption of the data by \< 0.04% in the 7MHz passband of
interest.

Beam pulse power at high frequencies can corrupt the data due to
aliasing. To minimize this, an additional 5 pole 0.01dB Chebyshev filter
with corner at 17MHz. This filter will provide an additional --37dB at
about 32MHz. The result is in excess of --80dB at the Nyquist frequency.
Therefore, beam spectral power aliased to base-band will be attenuated
by more than 1 part in 10,000 or 0.01% (1 lsb for a 14 bit ADC with sign
and 13 bit magnitude).

The sampling rate selected will also affect the computation of charge
since it is a digital integration of the current signal. A simulation of
a Simpson's Rule integration algorithm, and a simple sum was conducted
(by M. Kesselman (BNL), and independently by Alexander Aleksandrov
"Sasha" (ORNL)). This simulation places a typical HEBT current pulse
through a 5-pole 7MHz Gaussian filter, and computed the error in the
charge calculation.

Three sampling rates were analyzed, 16MHz, 32MHz, and 64MHz. One can see
from the plot below that to achieve \<0.1% error in the integral one
must sample at more than 25MHz. It is also interesting to note that the
error converges after 65MHz providing no advantage to using the more
computer intensive 3 point Simpson's rule. The difference is not very
much at lower sampling rates indicating that the simple sum can be used
with minimal loss of error. This analysis included time shifting the
input pulse to obtain the largest error.

Therefore, the choice of a 32 or 64MSa/s rate (at 2 or 4 times the
reference signal of about 16MHz) seems justified.

![](media/image11.jpeg){width="5.988194444444445in"
height="4.492361111111111in"}

**Anti-aliasing:**

The characteristics of the Gaussian filter or a Bessel filter are quite
broad, and offer about -43dB for the Gaussian, -47dB for the Bessel at
32MHz. To provide better filtering at the Nyquist frequency, a 17MHz - 5
pole 0.01dB Chebyshev filter has been added. This provides an additional
--37dB attenuation at 32MHz, for a total of \>-80dB. Additional
attenuation due to other amplifier stages further attenuates the signal
at 32MHz. This will yield better than 10,000:1, or more than 13 bits,
and provide adequate anti-aliasing.

**Gain Change:**

The large dynamic range requires a method to address signal amplitude
variation. Having finalized the transformer sensitivity to about 25mV
per 50mA peak current mini-pulse, yields a transformer output that could
go to 25 Volts in the Ring and RTBT. In addition, we need to allow some
"headroom" which has arbitrarily been established as a factor of two to
accommodate peaked pulse profiles (or maximum input voltage of 50V).

Initially we looked into switches to change gain. These switches must
handle the potentially large input voltage (50V). This narrowed our
search to relays, since fast semiconductor switches start to distort
near +30dBm. Relays suffer from slow response time, and are not well
suited to switching in nanoseconds. Alternate approaches were
investigated including:

-   Ping-pong amplifier schemes -- changing gain in one path while
    viewing the output of the other,

-   Building our own analog switches,

-   Providing protected input amplifiers in lieu of disconnecting with
    switches

-   Dual amplifier digitizer paths with digital multiplexing of ADC
    outputs

-   Switched amplifiers -- sometimes used in fast analog multiplexers,
    or power conservation circuits.

The ping-pong approach is a good approach to avoid losing a turn of
information. The semiconductor switches have proven to have voltage,
distortion and DC transmission problems. The relays are too slow.
Separate digitizer paths are too costly in board real estate, power and
money. The concept of protected amplifiers with switched amplifiers was
pursued.

An initial investigation of the number of gains required yielded 7 or 8
gains for 0.1% resolution. The resolution was relaxed to permit 4 gains.
Based upon a noise estimate for an AD6644 ADC (a +/- 1.1V, 13 bit plus
sign, 65MSa/s unit), ADC worst case noise is estimated at --72dB below
0.98V (-1dB Vmax) or 0.246mVrms, the minimum input signal to the ADC
should be 200 times (1/.005 for 0.5% resolution) the noise or 49mV ( a
ratio of 10.2 to achieve a peak signal of 0.5V or half scale). If a half
scale signal for 50Amps (25V input) is assumed, gain settings can be
estimated as follows:

TURN INPUT OUTPUT GAIN

Turn 1000 50A 25V ADC input = 0.5V Gain=0.02

Turn 98 4.9A 2.45V ADC input = 0.049V Gain=0.02

Turn 97 4.85A 2.425V ADC input = 0.5V Gain=0.1031

Turn 19 0.95A 0.475V ADC input = 0.049V Gain=0.10316

Turn 18 0.9A 0.45V ADC input = 0.5V Gain=1.1111

Turn 2 0.1A 0.05V ADC input = 0.0555V Gain=1.1111

Turn 1 0.05A 0.025 ADC input = 0.5 Gain=20

These initial estimates of gain were modified slightly (see below) after
considering amplifier protection circuitry noise and other amplifier
noise which modifies the initial estimate.

**Amplifiers and noise estimates:**

**ADC Pre-amp;**

The ADC6644 requires a differential input signal and an offset to about
2.5V since the ADC is a single supply device. The recommended driver is
an AD8138 which handles the DC shift and single ended to differential
drive conversion. It is matched to the ADC and delivers a wide bandwidth
(300MHz to match the ADC analog front-end) and low distortion. This
drive scheme improves noise immunity by the inherent common mode
rejection of the differential drive, and reduces harmonic distortion.
The differential amplifier is operated at unity gain to minimize
additional noise. The amplifier has a voltage noise of 5nV/rtHz and when
used with 4 - 500 Ohm resistors, the output noise expected is about
sqrt((5E-9\^2+5.7E-9\^2)\*(300E6))=131E-6V.

**Adjustable Gain Amplifier;**

Logarithmic amplifiers were eliminated due to their nonlinear transfer
function. It is desirable to have a linear system since we will be doing
digital processing. Although fixed gains will be used, the AD600, AD602,
and AD603 adjustable gain amplifiers were considered for computer
control of gain for flexibility. These amplifiers utilize a
well-controlled variable input attenuator with a fixed gain amplifier at
the output. This configuration works nicely providing variable gain
without affecting frequency response. The AD603 is a single
95MHz-bandwidth device, while the AD600 and AD602 are dual 35MHz
bandwidth devices. The 35MHz bandwidth is more matched to our needs. The
AD602 provides -10dB to +31dB gain per stage, and the AD600 provides 0dB
to 41dB gain per stage. They are pin compatible. These amplifiers have a
constant output noise due to the constant amplifier gain, with known
input ladder network impedance. The equivalent input noise of 1.4nV/rtHz
at the highest gain setting (or 158nV/rtHz at the output) is expected.
This will yield about 418uV noise at the amplifier output for a 7MHz
bandwidth.

Protection;

With signal inputs potentially as large as 50 V, one must consider
protecting the amplifiers. The AD600/AD602 has a maximum input voltage
limit of +/- 2V continuous and +/-Vsupply for 10ms. This amplifier is
difficult to protect with diodes since the diodes will distort input
signals as they get large. Attenuating the input to assure the signal
does not exceed +/- 2 volts requires an attenuation gain of 0.04. A
single turn providing about 25mV peak signal will be attenuated to 1mV
peak, and when amplified by the AD600 (G=100) will yield only 100mV
which provides an output s/n ratio of only about 200. This is marginal.

Placing a protected amplifier with known output limits, in front of the
AD600/AD602, will assure proper input voltage control. A protected
amplifier configuration incorporates low capacitance back-to-back diodes
at the input terminals of the amplifier to assure that the differential
input voltage does not exceed allowable limits (signals are held near
ground during normal operation). The input amplifier should be low
noise, provide a bandwidth commensurate with a 50ns rise time, and
provide good transient behavior. In addition, it is clear that the
gain-changing scheme will require attenuators. The attenuators must not
be affected by the changes in loading as the protection diodes saturate
with increased voltage. To accomplish this a number of amplifier
circuits were simulated using Pspice. The result was a need to limit
clamping diode currents to avoid exceeding diode and amplifier
differential input voltage limits. This lead to using a series 1K Ohm
resistor to a low capacitance HSMS2812 dual Schottky diode (2pF). This
large value of input resistance will generate significant noise, and
must be included in the noise estimates (see noise section).

To estimate the attenuator loading changes we assume the diode will drop
about 1 Volt, and a 3dB 150 Ohm pad is used to isolate the load from the
source. The pad is an 866-52-866 Pi pad. This is loaded at the source
end with two 150 ohm pads and a 50 ohm terminated line (the
transformer), and at the output by an appropriate 150 ohm load made up
from 176 Ohms and 1K plus diode as a load.

From "Reference Data for Radio Engineers" for a pad:

∆Z/Z = 2(∆Z~2~/Z~2~) / \[2N+(N-1) (∆Z~2~/Z~2~)\]; N is power ratio from
input to output

Therefore, for N=2 (3dB);

∆Z/Z = 2(∆Z~2~/Z~2~) / \[4+(∆Z~2~/Z~2~)\]

or: ∆Z~2~/Z~2~ = k\*4/(2-k) ; where k is a fractional error in the input
impedance.

For the case of 0.1% ie: k=0.001, we get ∆Z~2~/Z~2~ = 0.002 or 0.2%
change in load impedance will yield 0.1% change in input impedance.
Since there are three paths in parallel defining the load on the coax
line, this sensitivity is relaxed by a factor of 3.

For resistors R and R~L~ in parallel;

(∆R~p~/R~p~ ) = R/(R+ R~L~) (∆R~L~/R~L~ )

The load on the 3dB pad can vary as much as 0.6% and maintain a 0.1%
change of coax match.

For 35 Volts out of the 3dB pad (50 volts input), a one volt drop across
the diode will modify the effective input resistance
R\[V/(V-V~diode~)\]. The effective resistance change is about
R(V~diode~/V) or R/35 (2.857%). From this we can determine the resistors
we should use for the amplifier input. The minimum amplifier resistor is
713 Ohms with a pad terminator of 190 Ohms to achieve a maximum delta
resistance of 0.1% for the 50 Ohm cable termination.

The protected amplifier should provide a gain that would tend to
dominate the noise at this stage. It will also provide a maximum output
signal of about 4 volts requiring an attenuator of about 0.5 limiting
the signal to 2 volts as required by the AD600. A block diagram is shown
below.

Analog Block Diagram

**Switching amplifier matrix:**

The switching amplifier scheme uses a TI/Burr-Brown OPA680 series
amplifier. This amplifier can be switched off in 100ns and on in 25ns.
When this is used in a positive gain of two configuration, the feedback
and input resistors are effectively disconnected from the amplifier, and
the amplifier output can be represented as a 4pF capacitor. If this
feeds a summer, we can implement a fast switching amplifier selector
switch. The "Gap" time of 300ns in the signal with edges of about 50ns
leaves a period of about 200 ns to achieve proper switching without the
loss of a turn of data. The output capacitance and resistor load will
yield a time constant in the 6 ns range, which is far less than the
switching time. For this reason the OPA680 series has been considered as
the switching device. Each switching amplifier constitutes a separate
gain path for the signal. For the simplest data reduction afterwards,
separate offset adjustments to balance accumulated DC offsets in each
path are recommended. DC offset measurements should be made for each
gain path.

**Input attenuation;**

An input attenuator scheme was selected that distributed signals to
three major signal processing paths. The paths were chosen to have a 150
Ohm input impedance to yield a 50 Ohm match to the signal cable and
current transformer. One path delivers a sample of the signal to an
output port for high-speed data acquisition. A second delivers signals
to the high gain single turn signal path through a 150:150 ohms 3dB pad.
This feeds a protected amplifier since signals are expected to be as
high as 35V (0.707 \* 50V = 35V). The third path is an attenuator chain
that provides sufficient attenuation to permit using an AD600/AD602 with
no protection. This requires an attenuation gain of \<0.04; a gain of
0.03886 was selected yielding 1.94 Volts maximum. The amplifier will
make up the attenuator loss and provide a gain near 28. This path is
attenuated about 6dB (G=0.018868) to achieve a full scale output for 53V
input (1060 turns @ 100ma per turn).

**Max Gain of AD600/AD602 and Noise at ADC:**

If we assume unity gain through out all amplifier sections following the
AD600/AD602, we require a gain of 20/.707 = 28.3 (29dB) in the
AD600/AD602. Noise from the protected amplifier (see later,
approximately 8.4nV/rtHz) will be amplified to 8.4\*28.3 = 238nV/rtHz.
This added to the noise out of the AD602 is 285nV/rtHz. (sqrt(158\^2
+238\^2)). This noise when limited by a 7MHz Gaussian filter yields
755μVrms. The ADC noise has been estimated at 246μVrms. The resulting
noise at the ADC is 794μVrms. The signal will be 0.025\*20=0.5 V for S/N
ratio of 630 or a resolution of 0.16%.

**The protected amplifier:**

The higher gain paths will require protected amplifiers to assure that
the input levels are not exceeded. As pointed out earlier, the diode
protection requires about a 1K series resistor to assure that the diode
voltage and currents are kept low (for a BAS70 it is 1V at 17 ma; for an
HSMS2812 it is 1V at 35ma). This assures the diodes would properly
limit, and can support the signal levels.

The OPA 680 and OPA 620 voltage mode amplifiers were considered for a
protected amplifier stage. They are inexpensive, come in packaging of 1
(OPA680/OPA 620), 2 (OPA2680), or 3 (OPA3680) per IC, and provide
relatively wideband response (200MHz GBWP). The wide bandwidth is good
to allow a separate Gaussian filter to do most of the signal shaping
later on in the signal flow path.

Noise associated with the input resistor, and feedback resistor is
considerable with such large values as 1K for Rin and 4K for Rf (G=-4).

Noise associated with the 1K current limiting resistor, at 300 K, will
yield

E~1k~ = sqrt(4KTR)/rtHz

E~1k~ = 4.07nV/rtHz

The output noise of the amplifier is :

E~no~\^2 = (E~Ri~\*A~v~)\^2 + (e~n\*~(1+ A~v~ ))\^2 + (i~n-~\*R~f~)\^2 +
\[(i~n+~\*R~+~)\^2 + (E~R+~)\^2\]~\*~(1+ A~v~ )\^2 + E~Rf~\^2

> For; A~v~ = R~f~/ R~I~ ; K=1.38E-23 ; q=1.6E-19 ; f~c~=noise bandwidth
>
> E~Ri~=sqrt(4KTR~I~f~c~) ;
>
> E~R+~= sqrt(4KTR~+~f~c~) ;

E~Rf~= sqrt(4KTR~f~f~c~) ;

e~n~= amplifier equivalent input voltage noise ;

i~n-~= amplifier equivalent inverting input current noise
=sqrt(2qI~bias-~f~c~) ;

i~n+~= amplifier equivalent inverting input current noise
=sqrt(2qI~bias+~f~c~)

For the OPA680 -- Operating at an inverting Gain of 4 with R~i~ =1K,
R~f~ =4K and R~+~=0;

(noise= 6nV/rtHz, GBW=200MHz, 3.5pA/rtHz) voltage mode amplifier:

Optimum noise figure at Rs=En/In=1.7K Ohms

E~no~ = E~2k~\*A~v~ + e~n\*~(1+ A~v~ ) + i~n~(R~f~) =
sqrt\[(4.07\*4)\^2 + (6\*(1+4))\^2 + (0.0035\*4000)\^2 + 8.2\^2\]

E~no~ = 37.8nV/rtHz

For the OPA620 -- Operating at an inverting gain of 4 with R~i~ =1K,
R~f~ =4K and R~+~=0;

(noise=2.3nV/rt Hz, GBW=200MHz, 2.3pA/rtHz) voltage mode amplifier;

Optimum noise figure at En/In=Rn=1K Ohms

E~no~ = sqrt\[(4.07\*4)\^2 + (2.3\*(1+4))\^2 + (0.0023\*4000)\^2
+8.2\^2\]

E~no~ =23.4nV/rtHz

The OPA620 will provide about 2/3 the noise of the OPA680 when these
large resistor values are used and will be considered as the preferred
choice. The noise is amplified by the variable gain amplifier, which has
an inherent output noise near 158nV/rtHz, even though the gain will be
near 7.07 (28/4). It produces sqrt(165.5\^2 + 158\^2)= 229nV/rtHz at the
output of the AD600/AD602 set for a gain of 7.07 (total gain=
.707\*4\*7.07=20). For a bandwidth of 7MHz the resulting noise due to
the preamplifiers to the ADC system can be expected to be about 0.605mV.
This is added to the ADC noise of 0.246mV for a total of 0.653mV.
Therefore at this gain setting one would like to see a signal at the ADC
of about 200 times 0.65mV, or 130mV minimum.

From a noise consideration point of view, the protected amplifier
arrangement with a total gain of 20 will develop about 653uV noise
including the ADC. If we include an attenuator near 0.04, the protected
amplifier can be eliminated reducing the estimated noise to about 485uV
for the variable gain amplifier and ADC. As the total gain requirement
falls below 0.04 the variable gain amplifier can be removed reducing the
estimated noise to just that of the ADC or 246uV.

The single turn is expected to be about 25mV for a 50ma pulse providing
a signal to the ADC of 0.5V (20\*0.025). This provides a s/n ratio of
769 or 58dB. The minimum input level of 15ma will provide about 7.5mV
and will yield an ADC signal of 150mV or a s/n ratio of 230. Therefore,
the gain of 20 will work well for the first turn, and throughout the
MEBT, Linac and HEBT.

For use in the Ring, the variable gain amplifier gain can be reduced to
provide a s/n ratio of about 200 for the single turn case. This will
require a gain of 5.224 total. Therefore, gain is distributed as 0.707
for the attenuator, 4 for the protected amplifier, and 1.696 for the
variable gain amplifier. With this total gain, the signal will achieve a
level of about 0.5 volts at the ADC after turn 4. The next gain step
would eliminate the protected amplifier yielding a noise of 485uV, and
requiring a total gain of 0.776. This can be 0.03886 for the attenuator,
and 19.97 for the variable gain amplifier. The next gain change would
occur at turn 26. Gain for turn 27 to 276 is 0.0726. This would
eliminate the variable gain amplifier requiring a gain of 1.868 for the
preamplifiers. The gain required at turn 277 is 0.00707 which will be
useful till turn 1060, however, setting gain to 0.018868 will provide
the maximum s/n at the maximum number of turns.. This is reflected in
the table below.

**The resulting Gain Table is shown below:**

  --------- ---------- ---------- ---------- ---------- ------------ ------
  TURN      INPUT      INPUT      TOTAL GAIN ADC SIGNAL ESTIMATED    S/N
            CURRENT    VOLTAGE                          NOISE        

  1         50ma       25mV       20         0.5V       0.653mV      1555

  1         50ma       0.025V     5.144      0.1286V    0.643mV      200

  4         200ma      0.1V       5.144      0.5V       0.643mV      1555

  5         .6A        0.125V     .776       0.097V     0.485mV      200

  26        1.3A       0.65V      .776       0.5V       0.485mV      1040

  27        1.35A      0.675V     0.0726     0.049V     0.246mV      200

  276       13.8       6.9V       0.0726     0.5V       0.246mV      2032

  277       13.85A     6.925V     0.018868   0.130V     0.246mV      531

  1060      53A        26.5V      0.018868   0.5V       0.246mV      2032
  --------- ---------- ---------- ---------- ---------- ------------ ------

**Calibration:**

The calibration winding must be terminated in 50 Ohms to correctly
terminate the transformer for good transient response. A 50 ohm line is
required for both windings. It is planned that a separate current
calibrator will be used to generate pulses that approximate the
waveshape of the beam. Due to the 10 turns, only 1/10^th^ of the
simulated beam current is required. This is 5ma for the single turn case
in MEBT, Linac and HEBT, and a ramping or equivalent current of 5A peak
for the Ring. The lowest current measured on the highest range is 9.75A
requiring only about 1 Amp to simulate it.

We will monitor the current with a series resistor that is 0.1%
accurate. We can use Kelvin wired current shunts from Isotek
Corporation, 435 Wilbur Ave., Swansea, MA 02777 (508-673-2900). Isotek
makes ISA-PLAN precision resistors, of which their AN and A-H units are
available in 0.1% tolerances from 1mOhm to 100 Ohms. Data can be
filtered and digitized with a slow digitizer with 12 bit resolution at
the revolution rate near 1MSa/s.

A TI/Burr-Brown DAC2902 (12 bit current output) has been investigated as
a potential calibration source. This DAC provides 0 to 20 ma with a 1.25
volt compliance. To provide good cable termination for the calibration
winding, and no error in current delivered to the winding, a 49.9 Ohm
resistor in series with a 0.1 uF capacitor is used at the source end to
terminate the cable. This provides a 5 us time constant that represents
only 2% of the calibration signal delivered to the winding. Therefore,
long calibration pulses (of the order of 250us or more), and data pulse
strings suffer only slightly at the beginning. A 50 Ohm resistor in
series with the output of the DAC, with zener diode protection at the
DAC output, can provide DAC protection for large signals appearing on
the calibration winding.

Example of calibrator circuitry

APEX manufactures high voltage, high power amplifiers. The PA92 can be
powered by +/- 200 Volts and can deliver 4 Amps. The frequency response
of this unit, however, is about 100KHz at these levels. Therefore, the
current pulses for the higher ranges will be presented as a ramping
pulse train with pulse duration of the order of 20us. The transformer
will suffer some droop. The digital compensation should correct for the
droop and compute appropriate currents for comparison with the
calibrator. Alternatively, a current output DAC can be used to drive low
currents into a terminated cable (requires about 49 Ohms in series with
the calibration winding). Higher currents can be delivered by an audio
amplifier and signals in the audio range used for calibration.

The 50 Ohm termination required on the calibration winding offers a
problem during normal operation in the Ring and RTBT. With a 10 turn
calibration winding, the voltage expected on this winding is 1/5^th^ the
output winding voltage (10 Volts peak for 100A peak). A termination of
50 Ohms will dissipate 2 Watts peak, 0.04 Watts average.

Jullian Bergoz has pointed out that "standard" methods to deal with
calibration windings is to mechanically disconnect the winding to avoid
noise introduced by the calibration winding. This technique is a good
one for cases not requiring continuous calibration. It is not clear how
often the transformer must be calibrated, and this technique may be the
best solution to the problem.

Our experience, so far, indicates the transformer is stable for low
level inputs. This indicates the calibration technique is applicable for
MEBT, Linac, and HEBT. We have not yet applied large effective
calibration currents to determine the stability of the transformer to
large currents followed by small currents. Bergoz has indicated that he
expects the transformer to have residual magnetism in the core as a
result of the larger currents, and that this will probably cause
inductance changes. These inductance changes will affect the droop time
constant.

**Conclusions:**

A Bergoz FCT with 50:1 turns ratio matched to 50 Ohms, with a
sensitivity of 0.5V/A, a droop of 0.1%/us, and a 10 turn calibration
winding, will act as an appropriate transducer when coupled with digital
base-line restoration and droop compensation.

An approach involving switched gain paths must be used to accommodate
the very large signal voltage levels and gain changing requirements.
This method requires the use of protected amplifiers that use Schottky
diode protection across their input terminals. To achieve an
insignificant change to attenuator impedance as the diodes conduct and
selecting low capacitance diodes required the use of large resistors and
a --3dB attenuator. This results in significant noise introduced by this
stage. The signal levels are estimated to be large enough to accommodate
this noise when used with a gain of 20 for single turn operation or
throughout the MEBT, Linac, and HEBT.

The Ring and RTBT will require three additional gain changes to maintain
a near 200 s/n ratio. A gain table has been prepared indicating separate
gains at turn 1, 5, 27, and 277 for the Ring, while only two gains will
be used for the RTBT, one for studies and one for normal operation.
These gains can be switched between macro-pulses.

A calibrator will be designed to stimulate the calibration winding. A
current shunt will monitor the calibration current waveshape and
amplitude. A simple current output DAC will provide signals to calibrate
the two most sensitive gain paths. In addition, short circuit current
will be measurable off-line to assure proper operation of the
calibrator. The two high signal paths will be calibrated using an
amplifier capable of delivering about 4 Amps peak. This will be done
with a slower pulse.