Amplifier port requirements

Fig. 13 Interfacing of the signal source with the input port of the amplifier in cases in which the voltage of the signal source accurately represents the information, while the source impedance may be partly unpredictable.

The first step in amplifier design is to determine which electrical quantities must be used at the amplifier’s input and output ports. If the source and the load of an amplifier consist of transducers, we have to select the electrical port quantity that shows the best correspondence to the physical input or output signal of the transducer.

Fig. 14 Interfacing of the signal source with the input port of the amplifier in cases in which the current of the signal source accurately represents the information, while the source admittance may be partly unpredictable.

1. If the open circuit voltage of a signal source is accurately related to the primary physical information, we will model the signal source as a voltage source in series with its source impedance. This impedance may be complex and depend on the signal level and on the temperature. For accurate (unity-gain) transfer of the information from the signal source to the input port of the amplifier, the impedance of the input port of the amplifier should be infinite. This has been elucidated in Fig. 13.

2. If the short-circuit current of a signal source is accurately related to the primary physical information, we will model the signal source as a current source in parallel with its source impedance. The source impedance may be complex and depend on the signal level and on temperature. For accurate (unity-gain) transfer of the information from the signal source to the input port of the amplifier, the input impedance of the amplifier should be zero. This has been shown in Fig. 14.

3. If the voltage across the load is accurately related to the information provided by the load and the load impedance is inaccurately known, the output port of the amplifier should have zero output impedance to ensure that the information transfer does not depend on the load impedance. This is illustrated in Fig. 15.

   

   Fig. 15 Interfacing of the load with the output port of the amplifier in cases in which the voltage across the load accurately represents the information, while the load impedance may be partly unpredictable.

4. If the current through the load is accurately related to the information provided by the load and the load impedance is inaccurately known, the output impedance of the amplifier should be infinite to ensure that the information transfer does not depend on the load impedance. This has been shown in Fig. 16.

5. If the source or the load has an accurately known linear impedance, there is no preference for current or voltage as the electrical quantity at the input port or at the output port of the amplifier, respectively. In such cases, the current to voltage conversion or the voltage to current conversion by the source or the load impedance does not impose an error on the information to be processed.

   

   Fig. 16 Interfacing of the load with the output port of the amplifier in cases in which the current through the load accurately represents the information, while the load impedance may be partly unpredictable.

In all other cases, the transducer mechanism determines whether current or voltage shows the best correspondence to the information acquired by the sensor or delivered by the actuator.

The interfacing with some popular transducers has been described in the examples below.

Example

A PIN diode can be used as a sensor that converts optical power into electrical current. Study of the transducer mechanism shows that the short-circuit current of a PIN diode is accurately (linearly and instantaneously) related to the intensity of the light on the diode. The open circuit voltage across the PIN diode terminals shows both a logarithmic and a dynamic relation to the light intensity. This light intensity to voltage relation also strongly depends on temperature and is only partly reproducible due to fabrication tolerances. An accurate and reproducible conversion from the optical input quantity to the electrical output quantity is thus obtained when the short-circuit current of the PIN diode is taken as the electrical quantity.

Example

A microphone converts acoustical power into electrical power. The microphone is designed such that its open-circuit output voltage shows the best correspondence with the sound pressure.

Fig. 17 A microphone is designed such that its open-circuit output voltage shows the best correspondence with the sound pressure.

Example

An electric motor can be used as an actuator converting electrical signals into mechanical signals. Investigation of the transducer mechanism shows an accurate relation between the electrical current driving the motor and the torque it delivers. The electrical voltage shows the best relation with the angular speed.

Example

Piezoelectric transducers can be applied for the conversion of mechanical signals into electrical signals and vice versa. Study of the transducer mechanism shows the mechanical force is converted into electrical charge and vice versa. This charge can be measured by taking the open-circuit voltage at the output of the sensor, or by taking the time integral of the short-circuit current. Investigation of the transducer mechanism shows the latter method is more accurate, since the influence of the nonlinear Q-V relation of the transducer will then be negligible.

Example

Transmission lines and filters have to be driven from and/or terminated with accurate and linear impedances. There is no preference for either voltage or current as electrical input and output quantity.

Often, it is not directly clear which electrical quantity best reproduces the non-electrical quantity of the transducer and a study of the operation of the transducer is required to obtain this knowledge. Usually modeling, of sensors and actuators with the focus on information transfer is required to define proper interfacing with the amplifier and to define possible pre- or post-processing functions that compensate for predictable signal processing errors.

Based on the requirements for the port impedances of the amplifier, we will first define nine different amplifier types in section Amplifier types.

Amplifier types

In the previous section, we investigated the selection of the electrical quantity at the input port and at the output port of the amplifier. We found three possibilities for each port. For the input port, we have one of the following cases:

1. Sensing of the source current. The input port must behave as a short-circuit in which the current is sensed. The amplifier’s input impedance should be zero: \(Z_{i}=0.\)

2. Sensing of the source voltage. The input port must behave as an open-circuit and the voltage across the input port terminals must be sensed. In this case, the amplifier’s input impedance should be infinite: \(Z_{i}=\infty.\)

3. Sensing of current or voltage and termination of the source with an accurate linear impedance. The amplifier’s input impedance should now be accurately fixed to some characteristic value \(Z_{i}\). The voltage across this impedance or the current through this impedance can be used as the electrical input quantity of the amplifier.

For the output port, we have one of the following situations:

1. The load must be driven from a voltage source. The output port behaves as an ideal controlled voltage source. The output impedance of the amplifier should be zero: \(Z_{o}=0.\)

2. The load must be driven from a current source. The output port behaves as an ideal controlled current source. In this case, the output impedance of the amplifier should be infinite: \(Z_{o}=\infty.\)

3. The load must be driven from an accurate linear impedance \(Z_{o}\). The output behaves as a controlled voltage source with an accurate and linear impedance in series, or as a controlled current source with an accurate and linear impedance in parallel.

Based on the impedance requirements for both ports, nine amplifier types can now be defined. If they have zero reverse transfer (from the output port to the input port) they are called unilateral. The nine types are listed in Table 2.

Table 2 Amplifier types and their input and output port impedances.

no	amplifier type	source quantity	load quantity	\(\mathbf{Z}_{i}\)	\(\mathbf{Z}_{o}\)
1	Voltage amplifier	voltage	voltage	\(\infty\)	\(0\)
2	Transadmittance	voltage	current	\(\infty\)	\(\infty\)
3	Voltage to V/I	voltage	voltage or current	\(\infty\)	\(Z_{o}\)
4	Transimpedance	current	voltage	\(0\)	\(0\)
5	Current amplifier	current	current	\(0\)	\(\infty\)
6	Current to V/I	current	voltage or current	\(0\)	\(Z_{o}\)
7	V/I to voltage	voltage or current	voltage	\(Z_{i}\)	\(0\)
8	V/I to current	voltage or current	current	\(Z_{i}\)	\(\infty\)
9	V/I to V/I	voltage or current	voltage or current	\(Z_{i}\)	\(Z_{o}\)

According to the above, all amplifiers can be characterized by their transfer characteristics and their port characteristics. For an ideal

Linear, time-invariant and instantaneous.

voltage amplifier, these characteristics are shown in Fig. 18.

Fig. 18 Transfer and port characteristics of an ideal voltage amplifier with a voltage gain that equals \(tan(\alpha )\).

In section Summing and distributing signals we will find more arguments for selecting the proper amplifier type for a specific application. First, we first need to introduce the concept ground and study possible design consequences that follow from interconnections between the source, the load and the power supply. The ground concept will be introduced in section Ground, and design consequences that follow from interconnections between the amplifier ports will be discussed in section Port configurations.

Ground

In electrical systems, we often use the concept of the electrical ground, also simply know as the ground node or the ground.

In network theory, the ground is the reference node of a network. The voltage at other nodes is given with respect to the ground potential (see Chapter Network Theory (selected topics)). The absolute potential of the ground node itself cannot be defined and is simply assumed to be zero.

In real-world electrical systems, the electrical connection with the largest dimensions is usually taken to be the ground node. In most cases, this is a power supply terminal.

Port configurations

Until now, we did not consider whether one of the terminals of the source and/or load may be connected to the ground, or if both terminals should be floating with respect to the ground. At a first glance, its seems easy and straightforward to share the ground node; this is the case for example in cars. The ground is the metal chassis, and all devices like batteries, lamps, radio, etc. have one terminal connected to it. This simplifies the wiring: the metal chassis can be used as a return wire for all devices. However, in many situations, it is not possible nor desirable to use the ground as the common electrical connection for source, amplifier and load. Safety regulations in medical equipment or ground noise due to the physical dimensions of the ground connection and currents flowing through it may force us to use so-called floating input or output ports that do not share one of their terminals with the ground.

Regarding this aspect, we can define five different versions for each of the nine amplifier types listed in Table 2. Fig. 19 shows the five different port configurations with their commonly used names.

Fig. 19 Five different versions for each amplifier type.

Common-mode and differential-mode signals

The electrical behavior of ports that are floating with respect to the ground is not uniquely defined by the impedance between the two port terminals.

Let us, for example, consider the application depicted in Fig. 20A. There, a signal voltage source \(V_{s}\) with a source impedance \(Z_{s}\) has been connected to the floating input port of an amplifier.

Fig. 20 A signal source which is floating with respect to ground has been connected to the amplifier’s input port. Both terminals of the input port exhibit a equal, weak capacitive coupling to a noise voltage source.

Let us now assume that the signal source exhibits a capacitive coupling to a noise voltage source \(V_{n}\), which is referred to the ground. The coupling capacitance between the signal source and the noise source is \(C_{c}\). In Fig. 20B, this coupling is modeled by means of two capacitors, each with a value of \(\frac{C_{c}}{2}\), between the noise voltage source \(V_{n}\) and both terminals of the input port of the amplifier.

Fig. 21 Port definition with nodal voltages at the port terminals and currents flowing into the port terminals.

If both terminals of the input port exhibit an infinite impedance to the ground, the voltage of this noise source is found at both port terminals. Such a voltage is then called a \emph{common-mode }voltage: it is common for both inputs.\ In this case, we speak of a common-mode noise voltage at the input port, introduced by \(V_{n}\). Although this common-mode noise does not necessarily affect the so-called \emph{differential-mode }signal voltage between the two terminals, it may hamper the signal processing performed by the amplifier. This will, for example, be the case if this common-mode voltage becomes too large. In such cases, the amplifier will not be able to process the differential-mode input signal because the common-mode noise voltage drives the input port of the amplifier out of its linear operating range. A low port impedance would then be beneficial: it would attenuate the common-mode voltage of the port. At a later stage, we will show that common-mode and differential-mode port impedances can be designed independently.

Definitions of common-mode and differential-mode quantities

Fig. 22 Measurement setup for determination of: A: The common-mode port admittance B: The differential-mode port admittance The port can be an input port or an output port of a grounded circuit.

The definitions of the common-mode quantities and the differential-mode quantities below refer to the circuit in Fig. 21.

The common-mode voltage \(V_{cm}\) of a port is defined as the sum of the two terminal voltages of that port divided by two:

\[V_{cm}=\frac{V_{1}+V_{2}}{2}.\]

The common-mode current \(I_{cm}\) that flows into a port is defined as the sum of the currents that flow into the two-port terminals:

\[I_{cm}=I_{1}+I_{2}.\]

Fig. 23 Addition of currents requires parallel connections. All sources may be connected to ground.

The differential-mode voltage \(V_{dm}\) of a port is defined as the difference between the voltages at the two terminals:

\[V_{dm}=V_{1}-V_{2}.\]

The differential-mode current \(I_{dm}\) is defined as the difference between the currents that flow into the two-port terminals, divided by two:

\[I_{dm}=\frac{I_{1}-I_{2}}{2}.\]

Fig. 24 Distribution of voltages requires parallel connections. All receiving inputs may be connected to ground.

Fig. 22A and B show the test setup for determination of the common-mode and the differential-mode input admittances, \(Y_{cm}\) and \(Y_{dm} \), respectively.

The common-mode impedance \(Z_{cm}\) is the reciprocal value of \(Y_{cm}\), it is defined as:

\[Z_{cm}=\frac{dV_{cm}}{dI_{cm}}.\]

The differential-mode impedance \(Z_{dm}\) is the reciprocal value of \(Y_{dm}\), it is defined as:

\[Z_{dm}=\frac{dV_{dm}}{dI_{dm}}.\]

The port impedances from Table 2 refer to \(Z_{dm}\).

In section Modeling of the source and load isolation, we will introduce techniques for modeling the common-mode and the differential-mode behavior of the amplifier ports.

In Chapter Design of feedback amplifier configurations, we will present methods for designing amplifiers with specific port isolation properties and we will show the way in which the common-mode impedance and the differential-mode impedance of a port can be designed independently.

Summing and distributing signals

The need for addition (combination) and/or distribution of signals may also provide arguments for the selection of the information carrying electrical quantity. Fig. 23 shows the addition of currents in a common-ground system.

A common-ground system is a system in which all signal sources and loads share the ground terminal.

Addition of voltages requires voltage sources to be connected in series, which is not possible in a common-ground system. Similarly, distribution of voltages in a common-ground input-output system is much easier than the distribution of currents (see Fig. 24).