Analyzing analog signal chains to achieve higher performance: Application to transimpedance system

Introduction
The analog portion of the signal is becoming smaller and smaller as more and more digital signal processors (DSP) and microcontrollers are bringing their computational and timing strengths to analog signal chains. Having simplified the signal chain to a bare minimum, higher performance systems have been enabled by the use of digital techniques. This in turn has increased the requirements. Occasionally this can stress the limitation of the traditionally slow analog signal chain, pushing the analog bandwidths up.

Analog signal chains usually are separated into two categories: transmit (Tx) and receive (Rx). The complete signal chain, with both analog and digital components, is represented in Figure 1.

Figure 1: The complete signal chain showing the analog and digital blocks

Signal chains such as data acquisition or signal generator comprises either the Rx or Tx signal chain. Control loops and communication systems include both Rx and Tx signal chains.

In its simplest form, Rx signal chains usually comprise an amplifier, a filter, and an analog-to-digital converter (ADC) (Figure 2). The Tx signal chains usually compose a digital-to-analog converter (DAC), an anti-aliasing filter, and amplifier (Figure 3). The complexity of such a system can be increased when a multiplexer is designed to sample two or more channels simultaneously. Note that the sampling does not take place at the same time, but that the amplifier, filter and ADCs are shared to reduce cost.

It is not the intent of this article to develop a very complex system, but instead show the use of relatively simple techniques that allow the analysis of a much more complex system and derive useful models to optimize a given design.

Figure 2: The Rx signal chain block diagram

Figure 3: The Tx signal chain block diagram

To illustrate these techniques for the Rx path, in our example we use a transimpedance signal chain composed of an unity gain stable 230 MHz gain bandwidth product (GBWP) FET input operational amplifier (op amp), a first order filter, and a 10-bit, 60 Msps ADC. This system is represented in Figure 4.

Figure 4: The example signal chain with specified component parameters

When the analysis is complete, the limitations inherent to a transimpedance system will be clear.

Developing analytical tools
In a Rx signal chain, an amplifier realizes a conversion function. The most common functions are: high input to low output impedance, and current-to-voltage conversion. In this example the amplifier tends to have low noise and good DC precision. Depending on the circuit requirement, we select an amplifier with a suitable bandwidth.

In Tx signal chain, the amplifier tends to have high drive capability, good settling time, and/or low distortion.

Bandwidth consideration
With our amplifier selected, let’s take a look at how the amplifier’s bandwidth, filter and ADC analog bandwidth are combined. We consider each element as a first order response. Each equation is slightly different as we consider the various functions. The amplifier function, A(s), has a gain, G, and a pulsation, ω_A. The filter has a pulsation, ω_F, and the ADC has an analog bandwidth represented by the pulsation, ω_ADC, (Equation 1).

                        Equation 1

The combined calculations in Equation 1 express the overall system bandwidth.  The resulting function, H(s), is shown in Equation 2:

            Equation 2

Consider that the transimpedance amplifier (TIA) has a 50 MHz bandwidth. Also consider that the filter has a similar bandwidth of 50 MHz. Now consider that the ADC has a “track-mode input bandwidth” or analog bandwidth of 300 MHz. This means that the ADC pole can be neglected as the amplifier’s –3 dB bandwidth and filter dominate (Table 1).

Table 1: Bandwidth for each element and combined bandwidth

At this point of analysis, it is important to make approximations only to develop a simple analytical solution to increase the system understanding while developing in parallel a numerical solution that includes as much of the system as possible.

Reducing third-order to a second-order system
By approximating the system to be composed only of an amplifier and filter, we now can write H(s) in the standard form for a second order and derive both the characteristic pulsation, ω₀, and the quality coefficient, Q, of the function.

Equation 3

Keep in mind here that this approximation is only valid as long as the ADC’s bandwidth is much greater than the bandwidth of the TIA amplifier or filter.

Noise considerations
These results are particularly interesting as a second-order filter has a known equivalent brick-wall filter given the characteristic frequency and quality coefficient (Equation 4).

 Equation 4

Having established these relationships, we now can look into more details in the transimpedance signal chain and see how the selected devices are impacted.