SBOA538 February 2022 BUF802

Wide-bandwidth data-acquisition systems (for example, oscilloscopes and active probes) use an analog front-end (AFE) signal chain to capture high-frequency signals and fast-transient pulses. The key characteristics of a wide-band DAQ AFE include:

- Wide -3 dB bandwidth to measure a wide-frequency range of signals
- High-input impedance mode to prevent loading of the measured signals
- Low-noise to detect low-magnitude signals
- Superior distortion performance to maintain signal fidelity

When looking across the industry today
one can find a wide variety of amplifiers and buffers which support bandwidths
greater than 1 GHz, however, these bandwidths refer to the small-signal bandwidth (
< 100 mV_{PP}) and are not suitable to be used in an AFE, designed for
large signals (> 1 V_{PP}) in magnitude.

The BUF802 device is an open-loop,
unity-gain buffer with a JFET-input stage that offers low-noise, high-impedance
buffering for data acquisition system (DAQ) front-ends. The BUF802 supports DC to
3.1 GHz of bandwidth for a 1 V_{PP} signal while offering excellent
distortion and noise performance across the frequency range. The BUF802 can be used
in a composite loop circuit with a precision amplifier as shown in Figure 1-1 for
applications where wide-bandwidth and high-precision is desired.

This article explains tuning of the S-parameters, to achieve a flat frequency response and impedance matching for your front-end design.

A composite loop circuit interleaves two different and often complementary sub-circuits to create a single seamless circuit block whose resulting performance is a combination of each sub-circuits benefits. The composite loop in Figure 1-2 splits the input signal into low frequency and high frequency components, taking each signal component to the output through two different circuits (transfer functions) and recombines them to reproduce a net output signal. The Low-frequency path gives the net transfer function good DC precision and the BUF802 (High-frequency path) allows the net transfer function to achieve a wide-bandwidth. One of the challenges of the circuit in Figure 1-2 is to smoothly interleave the two paths to achieve wide-bandwidth as well as good DC precision. Any mismatch in the transfer functions of the two paths will lead to a discontinuity in the net transfer function frequency response resulting in a loss of signal fidelity. The BUF802 uses an innovative architecture to simplify the design challenges discussed previously of interleaving the two signal paths.

Scattering parameters or S-parameters
provide a framework for describing networks based on the ratio of input transmission
signals and reflected signals as shown in Figure 1-3. S_{11} represents ratio of the power reflected from port 1
(b_{1}/a_{1}, while a_{2}=0). S_{21} represents
ratio of the power transferred from port 1 to port 2 (b_{2}/a_{1},
while a_{2}=0). For a unidirectional device such as a buffer (with port 1 as
the input and port 2 as the output), S_{11} is the input port voltage
reflection coefficient describing the level of input-impedance matching while
S_{21} is the forward voltage gain and describes the frequency
response.

S-parameters are usually represented
as a function of frequency. For a detailed analysis of S-parameters check out the
blog *So, What are S-Parameters
Anyway?*

To achieve the desired S_{21}
across the frequency range the following conditions need to be met:

- Reduction of Peaking and Achieving Wide-Bandwidth
- Achieving Smooth Transition Between Low- to High-frequency

*Reduction of Peaking and
Achieving Wide-Bandwidth*

Figure 1-4 shows a composite loop circuit with input parasitics caused by the PCB and the
DUT (BUF802). The parasitic inductance of the PCB trace (L_{S}) can interact
with the input capacitance of the BUF802 (C_{IN}) to create a resonant LC
circuit resulting in a peaked frequency response as shown in Figure 1-5. To reduce L_{S}, minimize the trace length from the input port to the
BUF802s input. Figure 1-5 demonstrates the effect of a long trace on S_{21}.

The peaking due to the resonance
between L_{S} and C_{IN} can be dampened by the insertion of a
series dampening resistor R_{S} as shown in Figure 1-4. Besides helping in dampening S_{21} peaking, R_{S} also helps
with improvement of S_{11}. The exact math behind improvement of
S_{11} is discussed in *Tuning of the S _{11} Parameter*.

The series input capacitor
C_{HF} forms a voltage divider with C_{IN} reducing the gain of
High-frequency path. It is therefore important to make C_{HF} >>
C_{IN} to ensure the voltage divider does not attenuate the incoming AC
signals.

The BUF802 can achieve a -3 dB
bandwidth of 3.1-GHz for 1 V_{PP} signals. The addition of R_{S} to
reduce S_{21} peaking also reduces the bandwidth due to the addition of the
RC pole caused by R_{S} and C_{IN}. This effect is seen in Figure 1-6.

Table 1-1 summarizes the previous points.

Increasing R_{S} |
Decreasing R_{S} |
---|---|

Protects BUF802 against transients | Increases bandwidth |

Reduces peaking of S_{21} |
Improves S_{11} at lower frequency |

Improves S_{11} at higher frequencies |
Reduces output noise |

*Achieving a Smooth Transition
Between the Low- and High-Frequency Regions*

The BUF802 can be used as a standalone buffer, Buffer Mode (BF Mode), or in a composite loop with a precision amplifier. Composite Loop Mode (CL Mode), helps to achieve both DC precision and wide, large-signal bandwidth. Operating the BUF802 in CL Mode with a precision amplifier requires the S21 responses (Gain) of the two different sub-circuits to be matched to maintain a smooth transition between the low-frequency and high-frequency response. A smooth transition can be achieved by adhering to the following two conditions:

- α/β = G ( where α =
R
_{α2}/ (R_{α2}+ R_{α1}) , 1 /β = 1+ (R_{β2}/ RPOT) as shown in Figure 1-7 and G = DC Gain of BUF802) - High-frequency response pole
(f
_{HF})<< low-frequency pole (f_{LF})

For the first condition the low-frequency region is determined solely by the precision circuit. The incoming signal is divided down in amplitude by the ratio α and is further gained up by 1/β, by the precision amplifier. Therefore, in the low-frequency region:

Equation 1. S_{21} (at low-frequency) = α *
1/β

The Gain (G) can be found in the BUF802 data sheet and is typically 0.96 V/V.

Equation 2. S_{21} (at high-frequency) =
G

To maintain a constant S_{21}
across frequency make **G = α/β** by adjusting the value of RPOT.

The high-frequency pole of the BUF802
(f_{HF}) path is created by C_{HF} and R_{HF} as is
shown in Equation 3. The low-frequency pole (f_{LF}) of the precision amplifier path is a
function of the Gain Bandwidth Product (GBW) of the precision amplifier, the
auxiliary path gain (G_{AUX}) and the parasitic input capacitance of the
BUF802 and is shown in Equation 4.

Equation 3. f_{HF} = 1/ (2 × π ×
R_{HF} × C_{HF})

Equation 4. f_{LF} = GBW (precision
amplifier) × G_{AUX} × β

The composite loop transition region
should be designed so that the high-frequency pole (f_{HF}) falls at a much
lower frequency than the low-frequency pole (f_{LF}). This ensures a
sufficient overlap in the crossover frequency region and simplifies the complex
transfer function into simple poles and zeros.

In addition
to the two conditions mentioned previously C_{F} (compensation capacitor)
needs to be tuned to ensure sufficient compensation of the precision amplifier. The
C_{F} value is calculated using the formula in Equation 5.

Equation 5. C_{F}= C_{INPA} *(g
R_{α1}/R_{β2}-1)

where C_{INPA} is the common
mode input capacitance of the precision amplifier.

Figure 1-8 shows the effect of C_{F} tuning for its three different values.

Refer to section 9.2.1.2 in the BUF802 data sheet for the design procedure of a 1-GHz AFE using the previous equations.

Impedance matching is important to
reduce reflections and preserve signal integrity. An S_{11} better than -15
dB across the frequency of interest is considered an acceptable target spec. While a
50-Ω termination helps achieve the desired S_{11}, it is important to have a
high input impedance option to measure a signal without loading the previous driving
stage. Hence, data acquisition systems can have a selectable 50- Ω input and 1-MΩ
input termination option. The JFET-input stage of the BUF802 offers G-Ω’s of input
impedance and can therefore be terminated with an external 1 MΩ resistor without
affecting performance. If a 50 Ω termination is required it can be switched in via a
relay as shown in Figure 1-9. The BUF802 therefore has the flexibility to be used in both 1-MΩ and 50-Ω
terminated systems.

While it is possible to mount an exact
50-Ω termination to achieve the resistance at the input of the front-end composite
loop circuit, the parasitic capacitance of the BUF802 (C_{IN}) appears in
parallel with the 50-Ω resistance resulting in a non-ideal termination across
frequency.

The parasitic
input capacitance of the BUF802 (C_{IN}) is 2.4 pF. The input impedance of
the BUF802 at a particular frequency (X_{CF}) can be calculated using the
formula:

Equation 6. X_{CF} = 1/ (2π * f *2.4 pF)

Therefore, the net input impedance seen by the signal will be:

Equation 7. X_{CF} || 50 Ω

For example, at f = 1 GHz,
X_{CF} is equal to 66.3 Ω. Therefore, the net input impedance seen by
the signal is 66.3 Ω || 50 Ω = 28.5 Ω.

The addition of R_{S} (to
reduce S_{21} peaking), and, the addition of a series termination inductor
(L_{N}) (see Figure 1-10 ) results in a net input impedance as shown in Equation 8.

Equation 8. Net input impedance = (50 Ω +
X_{L}) || (R_{S} + X_{CF})

Where X_{L} = 2π * f *
L_{N}

With f = 1 GHz, R_{S} = 30 Ω,
L_{N} = 6.8 nH, C_{IN} = 2.4 pF and using Equation 8.

Equation 9. Input impedance = (50 Ω + 42.7 Ω) || (30
Ω + 66.3 Ω) ≈ 48 Ω.

While R_{S} can be increased
to bring the input impedance to an exact 50 Ω, we are limited by the maximum
R_{S} value as discussed in Table 1-1. Figure 1-11, shows
S_{11} vs frequency for different values of R_{S}.

- For more details on discrete
implementation design challenges and how the BUF802 alleviates these problems,
read the
*Simplify Analog Front-End Designs with Hi-Z Buffers*blog post. - BUF802 TINA-TI / SPICE model.
- The
*Flexible 3.2-GSPS Multi-Channel AFE Reference Design for DSOs, Radar and 5G Wireless Test Systems*illustrates the performance of the BUF802 in a composite loop AFE design with measurement analysis. - For more information on how to
set up the EVM, check out the
*BUF802EVM Video*.