Category: Basics

Getting Started with Open-Source CMOS Analog IC Design Toolchain
To begin working with open-source tools for CMOS analog IC design, all you need is a computer and a stable internet connection.

It is recommended to install Linux, as all of the essential tools run smoothly on Linux-based systems. Linux distributions are free, and if you are using Windows, you can easily set up a Linux environment through WSL (Windows Subsystem for Linux). For example, I am using Ubuntu on WSL.

Below are the main tools used in a typical analog IC design flow:
- Schematic Capture:
  xschem — https://xschem.sourceforge.io/stefan/index.html
- Circuit Simulation:
  ngspice — https://ngspice.sourceforge.io
- Layout Editor:
  Magic VLSI — http://opencircuitdesign.com/magic/index.html
- Open PDK:
  SkyWater SKY130 — http://opencircuitdesign.com/open_pdks/index.html
Integrating Xschem with SKY130

There are clear instructions available for setting up xschem with the SKY130 PDK:

Documentation:
XSCHEM SKY130 INTEGRATION

A detailed video tutorial is also available, covering xschem, ngspice, and SKY130 PDK usage from scratch:
https://youtu.be/bYbkz8FXnsQ?si=K5OG5g5v23BnFscz
November 16, 2025
MOSFET Small-Signal Characteristics
In this article, we extract the small-signal characteristics of MOSFETs using open-source and free available PDKs and CAD tools. The analysis is carried out using the SkyWater sky130 PDK, Xschem as the schematic capture tool, and Ngspice as the circuit simulator.

All tools (Xschem, Ngfspice, and sky130 PDK) must be installed properly on a Linux system. In this work, Ubuntu running under WSL is used. The installation procedure is discussed in a separate article.

The reader is assumed to have a basic understanding of MOSFET device physics and the fundamentals of MOSFET operation. Figure 1 illustrates the structure and symbols of NMOS and PMOS devices. In integrated-circuit design, each MOSFET has four terminals: gate (G), source (S), drain (D), and bulk (B). Modern CMOS technologies typically employ a p-type substrate; therefore, the bulk of all NMOS devices (except native devices) is tied to the substrate, i.e., GND or VSS. In contrast, PMOS devices are fabricated in isolated wells, allowing their bulks to be biased independently.

Figure 1: (a) structure of NMOS and PMOS, (b) symbols (from [1])

Operation regions:

A MOSFET behaves as a switch (ON or OFF) in digital design, but in analog design it operates in one of three regions:
- Cut-off (OFF): V_GS < V_TH and V_GD < 0
- Saturation: V_GS > V_TH and V_GD < V_TH
- Triode (ON): V_GS > V_TH and V_GD > V_TH
Note that the transition between these regions is smooth, especially near the threshold voltage.

Voltage – Current Characteristics:

To explain MOSFET operation, we review the V–I equations of an NMOS transistor. PMOS equations follow the same form.

Triode region (ON):

$I_D=\mu_nC_{ox}\frac{W}{L}\left[\left(V_{GS}-V_{TH}\right)V_{DS}-\frac{1}{2}V_{DS}^2\right] \qquad (1)$

For V_DS << 2(V_GS – V_TH):

$I_D\approx\mu_nC_{ox}\frac{W}{L}\left(V_{GS}-V_{TH}\right)V_{DS} \qquad (2)$

Saturation region:

Including channel length modulation,

$I_D=\frac{1}{2}\mu_nC_{ox}\frac{W}{L}\left(V_{GS}-V_{TH}\right)^2(1+\lambda\ V_{DS}) \qquad (3)$

The parameter λ is the channel-length modulation coefficient, which decreases with increasing channel length:

$\lambda\propto\frac{1}{L} \qquad (4)$

Second-order effects:

Body effect: Increasing the source-to-bulk voltage raises the threshold voltage:

$V_{TH}=V_{TH0}+\gamma\left(\sqrt{2\Phi_F+V_{SB}}-\sqrt{\left|2\Phi_F\right|}\right) \qquad (5)$

$\gamma=\frac{\sqrt{2q\epsilon_{si}N_{sub}}}{C_{ox}}\approx0.3\ to\ 0.4\ \left(V^\frac{1}{2}\right) \qquad (6)$

$V_{TH0}=\Phi_{MS}+2\Phi_F+\frac{Q_{dep}}{C_{ox}}=V_{TH}\ for\ V_{SB}=0 \qquad (7)$

Subthreshold (Weak Inversion) : When V_GS ≈ V_TH, the device enters weak inversion, and the drain current follows:

$I_D=I_0\exp{\frac{V_{GS}}{\xi V_T}} \qquad (8)$

where I₀ is proportional to W/L, and ξ > 1 and V_T = kT/q. We say the device operates in weak inversion in contrast with strong inversion.

Small-signal model:

Fig.2 shows the small-signal MOSFET model [1].

Figure 2: (a) Basic MOS small-signal model; (b) channel-length modulation represented by a dependent current source; (c) channel-length modulation represented by a resistor; (d) body effect represented by a dependent current source. [1]

Equations:

In triode region, a MOSFET behaves as a voltage-controlled resistor:

$R_{on}=\frac{1}{\mu_nC_{ox}\frac{W}{L}(V_{GS}-V_{TH})} \qquad (9)$

In saturation, the transconductance is:

$g_m=\frac{\partial I_D}{\partial V_{GS}} \qquad (10)$

Equivalent expressions include:

$g_m=\mu_nC_{ox}\frac{W}{L}(V_{GS}-V_{TH}) \qquad (11)$

$g_m=\sqrt{2\mu_nC_{ox}\frac{W}{L}I_D} \qquad (12)$

$g_m=\frac{2I_D}{V_{GS}-V_{TH}} \qquad (13)$

The output resistance due to channel-length modulation is:

$r_o=\frac{1}{g_{ds}}=\frac{\partial V_{DS}}{\partial I_D}=\frac{1}{\frac{1}{2}\mu_nC_{ox}\frac{W}{L}\left(V_{GS}-V_{TH}\right)^2\times\lambda} \qquad (14)$

For λV_DS << 1,

$r_o=\frac{1}{g_{ds}}\approx\frac{1+\lambda V_{DS}}{\lambda I_D}\approx\frac{1}{\lambda I_D} \qquad (15)$

The body-effect transconductance is:

$g_{mb}=\frac{\partial I_D}{\partial V_{BS}}=gm\frac{\gamma}{2\sqrt{2\Phi_F+V_{SB}}}=\eta\ g_m \qquad (16)$

where η is typically around 0.25

Simulation results:

Long-channel NMOS: The circuit in fig. 3 is used to evaluate the small-signal, low frequency behavior of an NMOS device. Because capacitances are not considered in this section, DC-sweep analysis is employed.

Figure 3: Simple NMOS circuit used for DC-sweep analysis

Here, the W/L is 100u/1.5u, number of gates (fingers) are 10, and the V_GS sweep is from 0 to 1.8V. Fig. 4 shows g_m and g_ds of the NMOS versus V_GS.

Figure 4(a)

Figure 4(b)

In this circuit, V_TH ≈ 560mv. As expected, by increasing V_GS, both g_m and g_ds increase. It’s interesting to see the g_ds– I_D relationship as shown in fig. 5. The curve is nearly linear, and according to (15), its slope is corresponds to the channel-length modulation coefficient λ.

Figure 5: g_ds vs. I_D

The intrinsic small-signal gain of a MOSFET is defined as

$A_v=g_mr_o=\frac{g_m}{g_{ds}} \qquad (17)$

Fig. 6 plots the gain vs. V_GS.

Figure 6: Intrinsic small-signal low-frequency gain of NMOS with W/L = 100u/1.5u

In this example of long-channel NMOS, the gain peaks at an overdrive voltage of V_ov = V_GS – V_TH ≈ 100 mV.

As V_ov (and thus I_D) increases, the gain decreases. Below V_ov ≈ 80 mV, the device is in weak inversion, and for V_GS < V_TH, the gain loses its physical meaning.

Short-channel (sub-micron) NMOS: For channel length below 1 um (sub-micron), the MOS device behavior is significantly affected by short-channel and higher-order effects. Figure 7 illustrates how these phenomena alter the small-signal parameters for a device with W/L = 10u/0.15u. Detailed discussion of short-channel devices will be provided in a subsequent article.

Figure 7(a)

Figure 7(b)

Figure 7(c)

Figure 7(d)

[1] Razavi, B., Design of Analog CMOS Integrated Circuits, 2nd ed. New York, NY, USA: McGraw-Hill, 2017.
November 15, 2025
Useful Stuff: Capacitor (part 2)

SRF:

A capacitor doesn’t always behave like a capacitor, especially at high frequencies. As shown below, the equivalent circuit of a capacitor includes a series inductance, known as the Equivalent Series Inductance (ESL). The ESL varies depending on the capacitor type, packaging, and physical dimensions.

Capacitor Model

At low frequencies, the impedance of the ESL (Z_L) is negligible compared to the impedance of the capacitor (Z_C):

$Z_L=2\pi fL$

$Z_C=\frac{1}{2\pi fC}$

As the frequency increases, Z_L increases while Z_C decreases. At high frequencies, the inductive impedance dominates, causing the capacitor to act more like an inductor. But what do we mean by “low frequency” and “high frequency”? How can they be distinguished?

At a specific frequency, the two impedances Z_L and Z_C become equal. This is known as the self-resonant frequency (SRF) of the capacitor:

$Z_L = Z_C$

$2\pi f L = \frac{1}{2\pi f C}$

$SRF = f = \frac{1}{2\pi \sqrt{LC}}$

Larger capacitors tend to have a lower SRF. This is why, in some cases, you may see a nano-Farad capacitor placed in parallel with a multi-micro-Farad capacitor. The smaller capacitor is used to maintain capacitive behavior at higher frequencies where the larger capacitor cannot.

October 21, 2024

Useful Stuff: Capacitor

Capacitor is a basic and one of the most important components in electronics.

Capacitors come in various types, each suited for specific applications. Here are some common types of capacitors:

Ceramic Capacitors: Widely used in electronic circuits for their small size and stability. They come in various temperature coefficients and voltage ratings.

Electrolytic Capacitors: Typically used for power supply filtering and energy storage due to their large capacitance values. They are polarized and have higher capacitance per unit volume compared to ceramic capacitors.

Tantalum Capacitors: Similar to electrolytic capacitors but offer better performance in terms of stability and reliability. They are also polarized and used in applications requiring high capacitance and low leakage current.

Film Capacitors: Known for their high precision, stability, and low loss. They are used in applications where a stable and reliable capacitor is required, such as in audio equipment and power electronics.

Supercapacitors (Ultracapacitors): Offer very high capacitance values and can store large amounts of energy. They are used in applications requiring rapid charge and discharge cycles, such as in energy storage systems and backup power supplies.

Mica Capacitors: Provide high precision and stability, often used in RF and microwave applications due to their low loss and high-frequency performance.

Polymer Capacitors: Similar to electrolytic capacitors but use a solid polymer electrolyte. They offer better performance in terms of ESR (Equivalent Series Resistance) and stability.

Variable Capacitors: Allow adjustment of capacitance value, commonly used in tuning circuits for radios and other communication devices.

Each type of capacitor has its unique characteristics and is chosen based on the specific requirements of the application.

ESR:

ESR (Equivalent Series Resistance) is an important characteristic of capacitors. In some applications like switching-mode power supplies (SMPS) this parameter plays a critical role to select the capacitor.

The capacitor model is shown below.

Some manufacturers produce capacitors specifically for low-ESR. The specifications of Low-ESR Series can be found in data sheets published by manufacturers. The table below shows some popular Low-ESR series of capacitors.

Manufacturer	Series	Style	Technology	Low ESR down to [mΩ @ 20ºC / 100kHz
AVX	TCJ	Chip	Polymer aluminium	10
AVX	TCQ	Chip	Polymer aluminium	25
AVX	TCM	Chip	Polymer tantalum multi-anode	6
AVX	TPS	Chip	Tantalum	25
AVX	TPM	Chip	Tantalum	12
KEMET	A700	Chip	Polymer aluminium	4.5
KEMET	A759	Radial	Polymer aluminium	12
KEMET	A768	SMD	Polymer aluminium	15
KEMET	T528	Chip	Tantalum multi-anode	4
KEMET	T520/T530	Chip	Tantalum multi-anode	4
Murata	ECAS	Chip	Polymer aluminium	6
Nichicon	GYB	Chip	Aluminium electrolytic	20
Nichicon	GYC	Chip	Aluminium electrolytic	20
Nichicon	PCH	Chip	Aluminium electrolytic	13
Nichicon	PCR	Chip	Aluminium electrolytic	13
Nichicon	UCM	Chip	Aluminium electrolytic	50
Nichicon	UCZ	Chip	Aluminium electrolytic	32
Panasonic	FN	SMD	Aluminium electrolytic	80
Panasonic	FT	SMD	Aluminium electrolytic	60
Panasonic	FS	Radial	Aluminium electrolytic	12
Panasonic	OS-CON™	Chip	Polymer aluminium	14
Panasonic	SP-Cap	Chip	Polymer aluminium	6
Panasonic	ZA	SMD	Polymer hybrid	20
Panasonic	ZC	SMD	Polymer hybrid	20
Rubycon	ZLH	Radial	Aluminium electrolytic	12
Rubycon	PC-CON	Chip	Polymer aluminium	4.5
Vishay	190 RTL	Radial	Aluminium electrolytic	17
Vishay	170 RVZ	Radial	Aluminium electrolytic	17

popular Low-ESR series of capacitors in the market. (Source: avnet.com)

August 8, 2024

Useful Stuff: Resistor

Resistor is a key component, especially in discrete Electronics. According to Ohm’s Law:

$V_R=R\times I_R$

the voltage across resistor equals the current passes through the resistor times the resistance R.

Regarding assembly, there are two types of packaging:
1. Through-hole
2. Surface-mount or SMD
These two types are shown below.

Through-hole Resistor

Surface-mounted Resistor (SMD)

You can find a lot of data about resistors on the Internet. Here, some essential and useful information is collected.

Colors:

To show the value of a through-hole resistor, usually color codes are used.

Resistor band colors. (Source: KiCad)

Tolerance:

Common tolerances of resistors are 5% and 1%. 5% resistors use E24 values and 1% resistors use E96 values. The E-series values table is shown below.

E-series values. (Source: KiCad)

power Rating:

Both through-hole and SMD resistors provides various packaging size regarding power rating. below the package size info for TH and SMD are shown respectively.

Through-hole package size. (Source: eepower.com)

SMD package size. (source: eepower.com)

August 3, 2024