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Current mirror

A current mirror is a fundamental analog circuit that replicates a reference input current to produce one or more output currents of equal or proportional magnitude, typically using matched bipolar junction transistors (BJTs) or metal-oxide-semiconductor field-effect transistors (MOSFETs) in integrated circuits.^[1] It operates on the principle that identical transistors sharing the same base-emitter voltage (for BJTs) or gate-source voltage (for MOSFETs) will conduct currents proportional to their device geometries when biased in their active or saturation regions.^[1] The reference transistor, often diode-connected, establishes the controlling voltage from the input current, which is then applied to the output transistor(s) to generate the mirrored current, enabling precise current sourcing or sinking with low input impedance and high output impedance.^[2] Current mirrors exist in various configurations to address non-idealities such as finite output resistance due to the Early effect in BJTs or channel-length modulation in MOSFETs.^[1]^[3] In BJT implementations, the simple current mirror uses two matched NPN transistors with connected bases and a diode-connected reference, yielding an output current I_{OUT} \approx I_{REF} \left(1 - \frac{2}{\beta}\right), where \beta is the current gain, though advanced variants like the Wilson or cascode mirrors improve accuracy and output resistance by minimizing voltage differences across the transistors.^[3] For MOSFETs, the basic mirror relies on the square-law characteristic I_D = \frac{1}{2} \mu C_{ox} \frac{W}{L} (V_{GS} - V_T)^2, with the output current scaled by width-to-length ratios, while cascode and low-swing cascode types enhance compliance voltage and matching for low-voltage applications.^[1] These circuits are indispensable in analog and mixed-signal integrated circuits for tasks like biasing operational amplifiers, transconductance amplifiers, and differential pairs, as they provide stable current references insensitive to process, voltage, and temperature variations when properly matched.^[1] Layout techniques such as common-centroid or interdigitated patterns minimize mismatch errors, achieving accuracies better than 1% in modern processes.^[1] Beyond traditional IC design, current mirrors find use in neuromorphic computing for synaptic emulation and in power management for current balancing.^[2]

Fundamentals

Basic Principle

A current mirror is an analog circuit block that produces an output current proportional to a reference input current, typically achieving a 1:1 ratio in its basic form.^[3] This functionality allows the circuit to replicate the input current at the output terminal, serving as a fundamental building block in analog designs for tasks such as current sourcing or sinking.^[4] The core mechanism relies on two or more matched transistors operating in the forward active region for BJTs or saturation region for MOSFETs, where the input branch sets the reference current to establish a shared bias voltage.^[3] The output transistor, biased by this same voltage, mirrors the current due to the identical characteristics of the matched devices, ensuring the output current closely follows the input under ideal conditions.^[5] In a simple schematic, the reference current passes through a diode-connected transistor, which generates the bias voltage at its gate or base; this voltage is directly coupled to the gate or base of the output transistor, enabling it to conduct a corresponding current through its drain or collector.^[3] As a prerequisite for broader analog circuitry, current mirrors provide essential biasing and enable efficient amplification by distributing precise currents across multiple stages.^[6]

Ideal Characteristics

In an ideal current mirror, the current transfer ratio, defined as k = I_{out} / I_{in}, equals 1 for symmetrically matched transistors, ensuring exact replication of the input current at the output. For non-unity ratios, k can be precisely set to n:m by scaling the emitter areas in bipolar junction transistor (BJT) implementations or the width-to-length (W/L) ratios in metal-oxide-semiconductor field-effect transistor (MOSFET) designs, allowing controlled current multiplication or division. This ratio arises from the identical bias conditions imposed on matched devices, where the shared base-emitter voltage V_{BE} for BJTs or gate-source voltage V_{GS} for MOSFETs enforces equal collector or drain currents, respectively. The output resistance R_{out} of an ideal current mirror approaches infinity, implying that the output current remains completely independent of the load voltage variations across the operating range. This infinite R_{out} eliminates any finite slope in the output current-voltage characteristic, providing a perfect current source behavior without degradation due to compliance voltage changes. The compliance voltage range in an ideal mirror spans from the minimum voltage required to maintain the forward active region for BJTs (approximately V_{BE}) or the saturation region for MOSFETs (V_{GS} - V_{th}, the overdrive voltage)—up to the breakdown voltage, allowing linear operation over an unlimited practical range without current distortion. The fundamental equation for an ideal 1:1 current mirror is I_{out} = I_{in}, derived from the transistor current equations under matched conditions: for BJTs, I_C = I_S \exp(V_{BE}/V_T) ensures equal currents with equal V_{BE}; for MOSFETs in saturation, I_D = \frac{1}{2} \mu C_{ox} (W/L) (V_{GS} - V_{th})^2 yields the same result with equal V_{GS}. Theoretically, these characteristics enable precise current replication, facilitating stable biasing in analog circuits without dependence on supply or load voltage fluctuations, thus serving as an ideal building block for differential amplifiers and active loads.

Non-Ideal Behaviors

Practical Approximations

In practical current mirrors, the assumption of infinite output resistance from ideal models is relaxed due to finite output resistance arising from the Early effect in bipolar junction transistors or channel-length modulation in metal-oxide-semiconductor field-effect transistors, which causes the output current to vary slightly with changes in the output voltage.^[3] This non-ideality results in a first-order model where the output resistance is on the order of tens to hundreds of kΩ, depending on the device parameters and bias conditions.^[7] A common approximation for the output current accounts for this voltage dependence symbolically as I_\text{out} \approx I_\text{in} \left(1 + \frac{V_\text{out} - V_\text{in}}{V_A}\right), where V_A represents the Early voltage (or its MOSFET analog, $1/\lambda).^[7] This model highlights how deviations from equal collector-emitter or drain-source voltages between mirror transistors lead to systematic current errors, typically less than 1-5% over the compliance range in well-designed circuits.^[3] Temperature variations further introduce non-idealities, as the base-emitter voltage V_\text{BE} in BJTs or gate-source voltage V_\text{GS} in MOSFETs decreases with increasing temperature (approximately -2 mV/°C for V_\text{BE}), causing the mirrored current to decrease without compensation.^[3] Basic uncompensated mirrors exhibit a temperature coefficient of approximately 0.1%/°C, reflecting the combined effects of thermal voltage scaling and saturation current changes.^[8] To mitigate mismatch errors in integrated circuit implementations, layout techniques such as common-centroid patterns are employed, where matched transistors are arranged symmetrically around the centroid of the layout to average out linear gradients in process parameters like threshold voltage or sheet resistance.^[9] This approach reduces systematic deviations to below 0.1% in precision designs by countering intra-die variations without altering the circuit topology.^[9] Current mirrors also impose bandwidth limitations, functioning as low-pass filters due to parasitic capacitances at the gates or bases interacting with the finite transconductance, yielding a gain-bandwidth product typically in the range of hundreds of MHz for sub-micron processes.^[10] This frequency response must be considered in high-speed applications to avoid signal distortion, with the dominant pole determined by the output resistance and load capacitance.^[10]

Error Sources

In current mirrors, transistor mismatch arises from process variations during fabrication, leading to deviations in key parameters that cause systematic offsets between the reference and output currents. For bipolar junction transistors (BJTs), variations in the current gain β result from differences in base doping, emitter area, or geometry, typically introducing relative errors of 1-5% in integrated circuits.^[11] Similarly, in metal-oxide-semiconductor field-effect transistors (MOSFETs), mismatches in the transconductance parameter μC_ox (W/L) stem from fluctuations in oxide thickness, mobility, or channel dimensions, yielding comparable 1-5% errors in standard CMOS processes for typical device sizes.^[12] Supply voltage dependence introduces another error source, as fluctuations in V_DD directly impact the stability of the reference current, particularly when the reference branch relies on a resistive divider from the supply. For instance, if the reference current is generated as I_REF ≈ (V_DD - V_BE)/R for BJTs or (V_DD - V_GS)/R for MOSFETs, a 10% change in V_DD can propagate a similar percentage variation to the output current unless buffered.^[13] This sensitivity, quantified as S = (V_DD / I_REF) · (dI_REF / dV_DD), ideally approaches zero but often reaches 0.1-1 in basic mirrors, degrading overall accuracy.^[13] Aging and reliability issues further degrade matching over time, especially in high-current applications. Electromigration in metal interconnects or contacts can alter resistance paths, causing gradual current drift in sustained high-current mirrors. In MOSFET-based mirrors, hot-carrier effects accelerate carrier injection into the gate oxide, shifting threshold voltage and reducing mobility, which may cause output current variations of less than 1% after prolonged stress in studied configurations.^[14] Noise contributions from the reference branch also propagate to the output, limiting precision in low-current or high-sensitivity applications. Thermal noise, arising from random carrier motion, and flicker (1/f) noise, due to trapping/detrapping at interfaces, generate current fluctuations that mirror directly to the output in well-matched pairs, with the total output noise spectral density approximately twice that of a single transistor. The relative error due to mismatch can be quantified as δI/I ≈ σ_ΔV_BE / V_T, where σ_ΔV_BE is the standard deviation of the base-emitter voltage difference between paired transistors, reflecting the impact of process-induced variations on exponential current relationships in BJTs; similar approximations apply to MOSFET threshold mismatches, with σ typically 1-5 mV leading to sub-percent errors in large-area devices.^[12] Temperature dependence exacerbates these effects but is often modeled within practical approximations for overall circuit behavior.^[12]

BJT Implementations

Basic BJT Mirror

The basic BJT current mirror employs two matched NPN bipolar junction transistors, Q1 and Q2, with their bases interconnected and emitters connected to ground. The input reference transistor Q1 is diode-connected by shorting its collector to its base, and the reference current I_\text{ref} is injected into this collector-base node. The output current I_\text{out} is sourced from the collector of Q2.^[7]^[6] The circuit operates by using I_\text{ref} to forward-bias Q1, establishing a base-emitter voltage V_\text{BE} that is shared with Q2 through the common base connection. This equal V_\text{BE} causes Q2 to conduct a collector current approximately equal to I_\text{ref}, thereby mirroring the reference current to the output. For matched transistors with high \beta, I_\text{out} \approx I_\text{ref}.^[7]^[6] For identical transistors with finite \beta = \beta_\text{in} = \beta_\text{out}, applying Kirchhoff's current law at the input node yields I_\text{ref} = I_{C1} + I_{B1} + I_{B2}, where I_{C1} = \beta I_{B1} and I_\text{out} = \beta I_{B2}. Since the shared V_\text{BE} implies I_{B1} = I_{B2} = I_B and I_{C1} = I_\text{out}, substitution gives I_\text{ref} = I_\text{out} \left(1 + \frac{2}{\beta}\right), so

I_\text{out} = \frac{I_\text{ref}}{1 + \frac{2}{\beta}}.

This equation accounts for base current diversion, with the approximation holding well when \beta \gg 2.^[7]^[6] The output transistor Q2 requires a minimum collector-emitter voltage to remain in the active region and avoid saturation, known as the compliance voltage, which equals the saturation voltage V_\text{CE(sat)} \approx 0.2\,\text{V} for typical silicon NPN BJTs at moderate currents.^[15] This simple two-transistor topology is widely employed for current biasing in discrete transistor circuits and integrated analog designs, such as differential amplifiers, where \beta > 100 yields I_\text{out} within approximately 2% of I_\text{ref}.^[6]

BJT Mirror Enhancements

To improve the performance of the basic bipolar junction transistor (BJT) current mirror beyond its limitations due to finite β effects, several enhancements address output resistance, compliance voltage, β mismatch, output swing, and linearity. These modifications leverage the current-driven nature of BJTs and their β dependence to achieve higher accuracy and robustness in analog circuits.^[3] The output resistance of the basic BJT current mirror, derived from the small-signal hybrid-π model, accounts for the shared base node between the reference and output transistors. With the input treated as an open circuit for small-signal analysis (fixed reference current), applying a test voltage v_x at the output collector yields an output current i_x influenced by the transconductance g_m, base-emitter resistance r_\pi, and output resistance r_o of each transistor. The resulting expression simplifies to R_{out} \approx r_o, where r_o = V_A / I_C is the intrinsic output resistance of the output transistor, with V_A the Early voltage (typically 50-100 V for standard BJTs).^[7]^[16] Emitter degeneration resistors added to both the reference and output branches extend the compliance voltage, allowing the mirror to maintain accurate current replication over a wider range of output transistor collector-emitter voltages V_{CE}. In the degenerated configuration, equal resistors R_E in each emitter create a voltage drop I_E R_E, shifting the base voltage to approximately V_{BE} + I_{REF} R_E. For the output transistor to remain in the active region (avoiding saturation), V_{CE} > V_{BE} + I_E R_E, where V_{BE} \approx 0.7 V and I_E \approx I_C for high β. This raises the minimum headroom required but stabilizes operation against V_{CE} variations by introducing local negative feedback, with the output resistance further boosted to r_O \approx r_o (1 + g_m R_E) \approx \beta (r_o + R_E) for large R_E \gg r_e (where r_e = V_T / I_E \approx 26 mΩ at room temperature). Typical R_E values of 100-500 Ω suffice for significant improvement in integrated circuits.^[3]^[7] To compensate for β mismatch between transistors, which causes systematic errors from unequal base currents diverting part of the reference current, a third transistor is added as a β helper or buffer. This auxiliary NPN transistor, configured as an emitter follower with its base connected to the shared base node, collector to the supply, and emitter supplying the bases of the mirror pair, amplifies the available base current by approximately β of the helper. The reference current now primarily sources the collectors of the mirror transistors, reducing the mirroring error from $2 / (\beta + 1) in the basic circuit to negligible levels (e.g., <0.1% for β > 100). This technique requires additional headroom of about V_{BE} for the helper but is widely used in precision analog ICs.^[3]^[16] High-swing versions of the BJT mirror employ buffering to lower the minimum output voltage V_{out} to the transistor's saturation voltage V_{CE(sat)} \approx 0.2 V, enabling greater signal swing in low-voltage applications. In the buffered configuration, the third transistor isolates the base node, preventing the output collector from pulling the bases into saturation prematurely. Without buffering, V_{out} must exceed V_{BE} to keep V_{CB} > 0; the buffer decouples this, allowing V_{out} to approach V_{CE(sat)} while maintaining active-mode operation and current accuracy within 1%. This is particularly beneficial in op-amp output stages or data converters.^[3]^[17] For improved linearity in the degenerated mirror, the output current follows I_{out} \approx I_{REF} \cdot (R_{sense} / R_{out}), where R_{sense} is the degeneration resistor in the reference branch and R_{out} is that in the output branch (ideally equal for 1:1 ratio). This relation arises from the voltage drops enforcing V_{BE1} + I_{REF} R_{sense} = V_{BE2} + I_{out} R_{out}, with V_{BE} nearly equal for matched devices; unequal resistors enable precise ratios (e.g., for Widlar sources), while equal values minimize Early effect nonlinearity by desensitizing I_{out} to V_{CE} changes. Simulations show <0.5% deviation over a 5 V V_{CE} range with R_E = 200 Ω at 1 mA.^[3]^[7]

MOSFET Implementations

Basic MOSFET Mirror

The basic MOSFET current mirror consists of two enhancement-mode NMOS transistors, M1 and M2, with their gates connected together and sources grounded. The input transistor M1 is diode-connected, meaning its drain is shorted to its gate, allowing a reference current I_\text{ref} to flow through it and establish the gate-source voltage V_\text{GS}. The output transistor M2 has its drain serving as the output terminal, from which the mirrored current I_\text{out} is sourced, while the shared V_\text{GS} biases M2 to replicate the current behavior of M1.^[18]^[19]^[20] For proper operation, both transistors must be biased in the saturation region, where the drain-source voltage V_\text{DS} satisfies V_\text{DS} \geq V_\text{GS} - V_\text{th} for each device, with V_\text{th} being the threshold voltage. The reference current through M1 follows the square-law model for saturation:

I_\text{ref} = \frac{1}{2} \mu_n C_\text{ox} \left( \frac{W}{L} \right)_\text{in} (V_\text{GS} - V_\text{th})^2,

which sets V_\text{GS} based on the applied I_\text{ref}. This V_\text{GS} is then applied to M2, yielding

I_\text{out} = \frac{1}{2} \mu_n C_\text{ox} \left( \frac{W}{L} \right)_\text{out} (V_\text{GS} - V_\text{th})^2 = I_\text{ref} \cdot \frac{(W/L)_\text{out}}{(W/L)_\text{in}},

assuming matched threshold voltages and process parameters between the transistors. Equivalently, defining the transconductance parameter k = \frac{1}{2} \mu_n C_\text{ox} (W/L) for each device (where \mu_n is electron mobility and C_\text{ox} is gate oxide capacitance per unit area), the output current simplifies to I_\text{out} = I_\text{ref} \cdot (k_\text{out} / k_\text{in}).^[19]^[20]^[19] The minimum compliance voltage at the output, or the lowest V_\text{DS2} for which M2 remains in saturation, is the gate overdrive voltage V_\text{OV} = V_\text{GS} - V_\text{th}, typically ranging from 0.1 V to 0.5 V depending on the bias current and device sizing. This low headroom makes the mirror suitable for low-voltage applications. In CMOS integrated circuits, the mirror's currents can be precisely scaled by adjusting the width-to-length (W/L) ratios of the transistors, enabling programmable reference currents without additional components and benefiting from on-chip matching for high accuracy.^[18]^[19]^[19]

MOSFET Mirror Enhancements

In MOSFET current mirrors, channel-length modulation introduces a non-ideality where the output current varies with the drain-to-source voltage, leading to finite output resistance. The output current can be expressed as I_{out} = I_{ref} (1 + \lambda (V_{out} - V_{ref})), where \lambda is the channel-length modulation parameter, typically ranging from 0.01 to 0.1 V^{-1} depending on the technology node and bias conditions. This effect results in an output resistance approximated by R_{out} = \frac{1}{\lambda I_{out}}, which enhances the mirror's performance in gain stages but requires compensation in precision applications to maintain current accuracy across varying output voltages. The body effect further degrades matching in MOSFET mirrors by altering the threshold voltage V_{th} when the source-to-body voltage V_{SB} differs from zero, particularly in n-channel devices where the body is tied to the substrate. To compensate, source followers can be employed to buffer the source potentials and minimize V_{th} variations, ensuring more uniform gate-to-source voltages across mirrored transistors. Alternatively, in processes supporting isolated wells (such as twin-tub CMOS), connecting the body terminal directly to the source eliminates the body effect, reducing V_{th} sensitivity to source voltage changes and improving mirror accuracy in integrated circuits. For low-voltage designs, improving output compliance—the minimum V_{DS} for which the mirror maintains accuracy—is critical to avoid saturation region violations. Level-shifting the gates of output transistors allows the minimum V_{DS} to approach the overdrive voltage V_{ov}, enabling operation near 0 V while preserving current fidelity, which is essential for supply voltages below 1 V in modern nanoscale processes. Device mismatch due to process variations limits the precision of MOSFET mirrors, with threshold voltage mismatch following Pelgrom's law: the standard deviation \sigma_{\Delta V_{th}} \propto \frac{1}{\sqrt{W L}}, where W and L are the channel width and length. Increasing the W/L ratio averages out local variations, reducing relative mismatch and enhancing output current accuracy, particularly in high-precision analog blocks like ADCs. Wide-swing cascode MOSFET mirrors address compliance and modulation issues by adjusting the gate-to-source voltage V_{GS} of the cascode transistors such that the output current remains independent of V_{DS} down to the overdrive voltage V_{ov} = V_{GS} - V_{th}. This configuration sets the bottom transistor's V_{DS} equal to V_{ov}, minimizing early saturation onset and extending the operable voltage range without sacrificing output resistance.

Advanced Variants

Feedback-Assisted Mirrors

Feedback-assisted current mirrors employ negative feedback mechanisms to enhance accuracy and output impedance beyond the limitations of basic transistor mirrors, often achieving near-ideal current replication with minimal error. In the basic configuration, an operational amplifier serves as an error amplifier, with a low-value sense resistor placed in the output current path. The input reference current generates a voltage across a reference resistor connected to the op-amp's non-inverting input, while the sense resistor's voltage is fed to the inverting input. The op-amp adjusts the gate or base voltage of an output transistor to equalize the voltages across the reference and sense resistors, ensuring the output current precisely matches the input current.^[21] The closed-loop operation yields a unity current gain, expressed as I_{out} / I_{in} = 1, independent of load variations. Theoretically, the feedback drives the output resistance R_{out} toward infinity, but practically, R_{out} \approx A \cdot R_{sense}, where A is the open-loop gain of the op-amp (typically $10^5 or higher) and R_{sense} is the sense resistor value (e.g., 1 Ω yields R_{out} \approx 100 kΩ). This high output resistance minimizes current variations due to output voltage swings. Additionally, the feedback extends the compliance voltage range to near rail-to-rail limits, limited primarily by the linearity of the op-amp and output transistor, allowing operation over a wider voltage span than passive mirrors.^[21] For integrated circuit applications, where discrete op-amps are impractical, transistor-only feedback variants replace the op-amp with simple amplifier stages composed of additional BJTs or MOSFETs. These configurations, such as gain-boosted mirrors, use a differential pair or common-source amplifier to sense and correct drain-source voltage mismatches, boosting output resistance to approximately A_v \cdot r_o, where A_v is the amplifier gain and r_o is the transistor output resistance (often exceeding 1 MΩ in modern processes). This enables seamless integration while maintaining high accuracy, with current errors below 0.01% achievable through precise transistor matching and feedback loop stability.^[22] Despite these advantages, feedback-assisted mirrors introduce drawbacks, including increased power consumption from the amplifier circuitry and added design complexity due to stability considerations (e.g., requiring compensation capacitors). However, the enhanced precision justifies their use in high-accuracy applications like precision instrumentation and low-noise analog ICs.^[21]^[22]

Other Specialized Mirrors

The cascode current mirror stacks transistors in both the reference and output branches to multiply the output resistance by approximately g_m r_o^2, where g_m is the transconductance and r_o is the intrinsic output resistance of a single transistor, thereby improving current matching by reducing channel-length modulation effects.^[23] This configuration yields an output current of I_{out} = I_{ref} (1 + \chi (V_{out} - V_{cas})), with \chi representing a small error coefficient dependent on process parameters.^[23] The Wilson current mirror employs a three-transistor topology with negative feedback to ensure operation largely independent of the transistor current gain \beta, resulting in I_{out} \approx I_{ref} even for finite \beta.^[7] Its structure features two mirroring transistors and a feedback transistor that equalizes collector-emitter voltages, enhancing output resistance through positive feedback mechanisms while maintaining a minimum compliance voltage of V_{CE(sat)} + V_{BE}.^[7] Depletion-load current mirrors utilize depletion-mode MOSFETs as active loads in the reference branch, enabling precise current replication in NMOS-only processes where enhancement-mode PMOS devices are unavailable. This approach leverages the normally-on characteristics of depletion transistors to provide a high-impedance reference current without requiring complementary devices. Current mirrors with gain deviate from unity ratios by employing unequal transistor sizing, yielding I_{out} = k I_{ref} where k is the width ratio of output to reference devices, or by integrating an operational amplifier for buffered scaling in precision applications.^[24] In high-voltage or precision analog circuits, topologies like the Wilson mirror deliver matching errors below 0.1% without trimming, owing to their feedback-enhanced stability and reduced sensitivity to process variations.^[25] Recent advancements include high-precision current mirrors based on two-dimensional materials, such as transition metal dichalcogenides, which offer improved matching and reduced power consumption in nanoscale applications as of 2024.^[26]

References

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This circuit copies the input current to the output and reverses its direction. It is appropriately named a current mirror. The circuit has just two ...
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In IC design we often assume that we have one precise current source and we copy its value to our circuits. 5. Page 6. Simple Current Mirror.
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This paper presents a comprehensive mismatch model for vertical BJTS, valid over bias, geometry, and tempera- ture. Mismatches in gain and collector and base ...<|control11|><|separator|>
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[14]
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⇒ BUILD CURRENT SOURCES FROM ACTIVE DEVICES! EXAMPLE: TO BUILD A 100KN RESISTOR. DIFFUSION WITH Rs. = 100 R/D.Missing: schematic | Show results with:schematic
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A discrete option for a current source is an op amp driven circuit is shown in Figure 3. ... The voltage at the input of the feedback op amp increases ...
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Compared to a simple current mirror circuit, the second design requires ... In addition to the efforts to boost rout, other techniques have been developed ...
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### Summary of Cascode Current Mirror from the Paper
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Aug 9, 2025 · A high performance operational amplifier 300 mil/SUP 2/ in area has been designed and fabricated in a standard n-channel silicon-gate enhancement/depletion MOS ...
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However imperfections in the CMOS processes lead to random and systematic errors in devices. Using large devices a current matching upto 0.1% can be achieved.