The input and output impedance are important parameters that describe how a circuit interacts with the signals and devices connected to it.
The input impedance indicates the impedance seen by a signal connected to the input terminals of the circuit. It determines how much current the circuit will draw from the signal source.
The output impedance of a circuit is the impedance presented to the load, the next stage or the block connected to the output terminals of the circuit. It indicates how much the circuit can drive the load effectively without significant voltage loss.
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High and Low Impedances…. Why?
Often, specifications describe the circuit properties with sentences such as “high input impedance” or “low output impedance” to describe the properties of a circuit… let’s understand what these terms mean.
Output Impedance
The ideal cases are an ideal voltage source with zero impedance (Rout = 0) and an ideal current source with infinite impedance (Rout ≈∞).
As typically output voltage mode is used, a low output impedance is considered as the best.
Summarizing:
- Current mode output → High impedance.
- Voltage mode output → Low impedance.
- RF → Matched impedances
- High Speed TL →Matched impedances
- Maximum power transfer → Matched impedances
Low Output
The main reason for a circuit to have low output impedance is to drive external “heavy” loads. With low output impedance, the circuit can deliver the required current with minimal significant voltage drop. Therefore, it maintains the signal integrity and prevents signal distortion at the output voltage.
For example, the source follower stage has a low output impedance.
- In general circuits, a low output impedance allows faster signal transitions in voltage output mode, when the circuit needs to respond to rapid changes in the input.
- In digital circuits, a low output impedance is important for driving capacitive loads. It minimizes the RC time constant and allows for faster transitions, providing better high-speed performance.
High Output
Complementary to the low output impedance, for a current-mode output (less common), a high output impedance is preferred to minimize current loss.
Circuits designed to source a constant current, for example DACs, require high output impedance. Additionally, in applications that need isolation or buffering between stages.
Input Impedance
High Input
High input impedance is the key to the success of CMOS technologies compared to BJTs. It minimizes the loading effect on the source circuit, drawing almost zero current from the source and preserving signal fidelity.
The input resistance of the MOSFET’s gate terminal is extremely high. It is typically considered infinite at low frequencies.
One of the main differences between voltage-controlled and current-controlled devices is the input impedance. Since BJT transistors need a base current to be managed, MOSFETs can be controlled without leaking current, unlike BJTs.
Low Input
This case is not really frequent, but in certain cases, a low input impedance is required. The most common case is to match the input impedance with another circuit or component.
For example, a 50Ω antenna or transmission line. Also, a resistive sensor signal interface requires a low input impedance to enable maximum power transfer from the sensor to the circuit.
The common-gate amplifier has a low output impedance.
Impedance Matching
Impedance matching is important for effective interfacing with other stages, circuits or components. This ensures efficient power transfer and avoids signal reflections.
In Radio Frequency (RF) or high-speed data communication interface circuits, impedance matching is important to avoid signal reflections, which can cause distortion, introduce unwanted noise, reduce the bandwidth and result in signal loss.
For matching impedance between stages, it is typical to use a lower characteristic impedance. In RF and communication circuits, the standard is 50Ω.
For a maximum and efficiently power delivery from a source to a load, the impedances must be matched for a maximum power transfer. For example, in solar cells, the MPPT algorithm is responsible for adapting the input impedance of the circuit to match the impedance of the solar cell and thereby achieve maximum power transfer.
Simple Stage Impedance Converters
The impedance of a circuit, as seen from a specific port, can be adapted or modified. The most common and simplest structures for transforming impedance are:
Source Follower Stage
Source Follower stages, also known as Common Drain, convert impedance from a high input impedance to a low output impedance.
Common Gate Stage
CG converts the impedance of a port from a low input impedance to a high output impedance.
The inverse of the transconductance (1/gm) is in the range of 50Ω or 100Ω, so the input impedance is considered, in general cases, low.
Cascode Structure
Adding cascodes to the circuit branches increases the output resistance of the original structure. For example, in a Common Source Structure, it adds an intrinsic gain multiplying factor to the output resistance. gm·ro of the new cascoded transistor.
The intrinsic gain of a device M2 is gm2·ro2
Voltage Buffer
A voltage buffer can be built using an operational amplifier connected as a unity-gain buffer. The voltage buffer is designed to drive low-impedance loads at high speed with minimal power consumption, replicating its input signal to the output regardless of the external conditions at the output.
The input impedance is very high (due to the MOSFET gate) and the output impedance is low.
Typical values of Output Impedance and Transconductance
For general cases, the range of these parameters: can be summarized as follows:
- The output resistance of a MOSFET is typically in the range of tens to hundreds of k𝛀, up to 1M𝛀.
- The transconductance of a MOSFET is in the range of millisiemens (mS) to a few hundreds of millisiemens.
Advanced nodes (14 nm, 7 nm, etc.) typically have higher gm and lower ro compared to older nodes (180 nm, 65 nm) due to reduced channel lengths and higher drive currents.
- The transconductance gm increases with higher bias currents, while ro decreases with higher drain currents.
- Larger devices, with wider channel widths, have higher gm but lower ro.
1/gm parallel to ro
It is common to find the inverse of the transconductance (1/gm) in parallel with the output resistance (ro). In such cases, it is common to consider only 1/gm and neglect ro to simplify the calculations.
Applying the previous typical values mentioned earlier, let’s suppose that the gm is 1 mS and the output resistance ro is 100K𝛀. This results in a parallel combination of 2 resistors: 1K𝛀 (1/gm) and 100k𝛀 (ro).
Since the 100k𝛀 resistance can be neglected in this case, the output resistance results in a 1k𝛀 output resistance. For an exact calculation, the corresponding output resistance would be 990𝛀.
How to Calculate the Output Impedance?
There are several methods to calculate the output resistance of a circuit. The most common technique for standard and simple circuits is the calculation by inspection.
For more complicated circuits, an auxiliary voltage source Vx is used. The input or output resistance of any circuit can be calculated easily.
A voltage source (Vx) is placed at the port of interest, with an output current (ix) entering the circuit. All the independent sources are set to zero (current sources are opened and voltage sources are shorted).
The output impedance is then calculated using the formula: Rout = Vx/ix
Conclusion
The input and output impedance of a CMOS circuit are key parameters that determine how the circuit can interact with the next connected components and stages.
High input impedance ensures minimal loading effects to the previous stages, preserving the signal fidelity. The low output impedance allows efficient power delivery and faster signal transitions.
