Why do we use SC-Resistors? Hands on Implementation in Cadence

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Often resistors with large resistance values are implemented on chips by switches and capacitors as switched-capacitor resistors.

The resistance, by definition, is a measure of how much a component opposes the flow of current (or discrete charges) in a period of time given a certain voltage difference.

A switched-capacitor resistor (SC-resistor) transfers the charge from the input to output as discrete pulses, not continuously as real resistors do.

Here the question is…

Why do we need SC-resistors in integrated circuits?

The quick answer: switched-cap resistors occupy much less silicon area. Large resistors, let’s say over 10Mohm cost a sizable amount of silicon area… and area is money!!

Another key feature is that the equivalent resistance ohmic value can be adjusted by changing the switching frequency.

Switched-cap resistors are used to implement high ohmic resistance at low area-cost. For example, to build RC filters.

SC-Filters have 2 big advantages:

1 Silicon area saving

2 Through the variable resistance, which is controllable by the input frequency, the cut-off frequency is therefore easily adjusted.

Advantages and Disadvantages of SC-Resistors

Pro

Less silicon area

Variable resistor controllable through the switching frequency

Trimmable through the frequency

It is said that we can set precisely on the order of 0.1% a SC-resistor, while the “regular” resistors ohmic values can vary by as much as 20% due to process variations.

Cons

Circuit much more complex

Necessary a non-overlapping signal generator block

Necessary an oscillator or clock source

Attention to the distribution of the clock phases inside the IC. It must be routed carefully and they can generate undesired couplings and cross-talk.

Introduce noise in the switching frequency + harmonics.

How is a SC-Resistor built?

Let’s start with the circuit implementation.

By definition, a switched-capacitor resistor is a discrete version of a standard traditional resistor (for example the rpoly).

The equivalent resistor value depends only on the ratios between capacitances and the switching frequency.

The schematic can be found in the following diagram:

Note that after the last switch+cap module, we add an extra final switch.

The switches are implemented as T-Gates.
The capacitor value is often reduced, in the order of 50 – 200fF.
A common number of stages can be between 8 and 16.

To build this circuit and have a nice and fast layout, it is usual way to create a fundamental building block involving a switch and a capacitor, and replicate it in series.

Clocking

To operate the Switched Capacitor Resistor, we need 2 clock phases and their negative counterpart.

Let’s call them A and B or CLK_A and CLK_B. Also, CLK_A_n and CLK_B_n.

For this implementation, we suppose that we have available an oscillator or any kind of clock source in the circuit. In this case, we will use an ideal clock oscillating at fclk frequency.

The required signal generator block must include a non-overlapping module, any kind of mechanism of power down or reset and most probably a light signal amplification power stage. Often, the signal amplification is included inside the SC-Resistor hierarchy.

T-Gate Switches

The implementation of the switches is made with “transmission gates” blocks.

Equivalent Resistor Calculation

The math formula of the equivalent resistance can be estimated based on the charge conservation principles. The formula is:

R = numberOfStages / (C_stage x fclk)

The explanation of where this magic formula comes from is detailed, including the full math development, in this article.

Summarizing:

The larger the capacitors, the lower the equivalent resistance
The faster it switches, the lower equivalent resistance

Simulation Test Bench

To test the resistance I set the SC-resistance itself plus a non-overlapping block. As a load I put a high ohmic resistor (1GOhm) plus some small capacitance (20fF).

To the input of the SC-resistor, I set an ideal vdc voltage source at 1.45V. Vdd is at 1.8V.